5) In the figure, triangle ABC is a right triangle at B. If CD = 15, find BC to the nearest tenth.

5) In The Figure, Triangle ABC Is A Right Triangle At B. If CD = 15, Find BC To The Nearest Tenth.

Answers

Answer 1

Answer:

BC ≈ 4.0

Step-by-step explanation:

∠ DCA = 180° - 70° = 110° ( adjacent angles )

∠ DAC = 180° - (30 + 110)° ← sum of angles in triangle

∠ DAC = 180° - 140° = 40°

Using the Sine rule in Δ ACD to find common side AC

[tex]\frac{AC}{sin30}[/tex] = [tex]\frac{15}{sin40}[/tex] ( cross- multiply )

AC × sin40° = 15 × sin30° ( divide both sides by sin40° )

AC = [tex]\frac{15sin30}{sin40}[/tex] ≈ 11.668

Using the cosine ratio in right triangle ABC

cos70° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{11.668}[/tex] ( multiply both sides by 11.668 )

11.668 × cos70° = BC , then

BC ≈ 4.0 ( to the nearest tenth )


Related Questions

Sine, cosine, and tangent are used when looking for a missing side length in the right triangle. True or False

Answers

I’m pretty sure it’s true

Maggie has 7 bills, all tens and twenties, that
total $100 in value. Find the number of tens, x, and
the number of twenties, y, that Maggie has.

Answers

Answer:

4 tens, 3 twenties

Step-by-step explanation:

4 tens  ($40) and 3 ($60)  twenties work. I’m sorry I don’t have a formula for it though.

the volume of a large aquarium is 210 ft. it is 5 ft wide and 6 ft high. what is the length of the aquarium?

Answers

The volume of a large aquarium is 210 ft. Is

Answer:

7

Step-by-step explanation:

210=5×6×x

x is length of aquarium.

210÷(5×6)=7

$/sqrt{9}$

Find the area of the shaded segment VB and length of VB

Answers

Answer:

Area of length Vb = 25 square units

Area of segment Vb  = 26 square units

Step-by-step explanation:

Area of length Vb = theta/360 * 2πr  

Area of length Vb = 120/360 * 2*3.14 * 12  

Area of length Vb = 1/3 * 75.36  

Area of length Vb = 25 square units  

Ares of length Vb is 25.1 sq. units

Area of shaded portion = Area of sector VUB - Area of triangle VUB

Area of sector VUB = theta/360 * πr²

Area of sector VUB = 120/360 * 3.14*144

Area of sector VUB = 1/3 * 452.16

Area of sector VUB =150.72

Area of triangle VUB  = r²sintheta

Area of sector VUB = = 12²sin 120

Area of sector VUB = = 144(0.8660)

Area of sector VUB = 124.71

Area of the shaded segment = 150.72 - 124.71

Area of the shaded segment = 26.01

Area of the shaded segment = 26 sq. unitsAnswer:

Area of length Vb = 25 square units

Area of segment Vb  = 26 square units

Step-by-step explanation:

Area of length Vb = theta/360 * 2πr

Area of length Vb = 120/360 * 2*3.14 * 12

Area of length Vb = 1/3 * 75.36

Area of length Vb = 25 square units

Ares of length Vb is 25.1 sq. units

Area of shaded portion = Area of sector VUB - Area of triangle VUB

Area of sector VUB = theta/360 * πr²

Area of sector VUB = 120/360 * 3.14*144

Area of sector VUB = 1/3 * 452.16

Area of sector VUB =150.72

Area of triangle VUB  = r²sintheta

Area of sector VUB = = 12²sin 120

Area of sector VUB = = 144(0.8660)

Area of sector VUB = 124.71

Area of the shaded segment = 150.72 - 124.71

Area of the shaded segment = 26.01

Area of the shaded segment = 26 sq. units

A ball is launched from a platform. The equation for the ball's height h at time t seconds after launch is h(t)= -16t^2+153.6t +393.12, where h is in feet. What is the initial height of the ball before launch?

Answers

Answer:

The initial height of the ball before launch is 393.12 feet.

Step-by-step explanation:

The ball's height ([tex]h[/tex]), in feet, as a function of time ([tex]t[/tex]), in seconds, is represented by [tex]h(t) = -16\cdot t^{2}+153.6\cdot t + 393.12[/tex]. The initial height of the ball before launch is the height of the ball evaluated at [tex]t = 0\,s[/tex]:

[tex]h(0) = -16\cdot (0)^{2}+153.6\cdot (0) + 393.12[/tex]

[tex]h(0) = 393.12\,ft[/tex]

The initial height of the ball before launch is 393.12 feet.

help help i need help with my math

Answers

Answer:

13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

48-[(2^2+3)x5]

48-[(4+3)x5]

48-[(7)x5]

48-[35]

13

is each pair of lines parallel perpendicular or neither​

Answers

Answer:

perpendicular, parallel, neither, parallel

What is the first quartile and third quartile of this data set: 34, 34, 36, 39, 50, 41, 45, 47, 40?

Answers

Answer:

http://web.mnstate.edu/peil/MDEV102/U4/S36/S363.htmlStep-by-step explanation:

Answer:

First quartile: 35

Third Quartile: 46

Step-by-step explanation:

A population of 350 animals has a growth rate of 5% each year. Write an exponential function to model this situation.

Answers

Given:

The population of animals = 350

Growth rate = 5% each year.

To find:

The exponential function to model this situation.

Solution:

The general exponential growth model is:

[tex]f(t)=a(1+r)^t[/tex]

Where, a is the initial value, r is the growth rate in decimal and t is the time period.

Substituting [tex]a=350, r=0.05[/tex] in the above formula, we get

[tex]f(t)=350(1+0.05)^t[/tex]

[tex]f(t)=350(1.05)^t[/tex]

Therefore, the required exponential function is [tex]f(t)=350(1.05)^t[/tex], where f(t) is the number of animals after t years.

hi! i’ll give brainliest please help

Answers

Answer:

third option mechanical weathering

Step-by-step explanation:

in mechanical weathering it breaks the rock into smaller pieces . these smaller pieces are just like the bigger rock , just smaller .

GIVING BRAINIEST IF CORRECT!!!
Mr. Cohen just got a pool and decided to fill it up using a hose. After a half hour, the pool is filled 1/15 of the way. How much will the pool be filled after 6 hours?
A. 4/5 full
B. 1/30 full
C. 2/5 full

Answers

Answer:

C. 2/5 full

Step-by-step explanation:

[tex]\frac{1}{\frac{1}{15} } :\frac{6}{y}[/tex]

y · 1 = 1/15 · 6

y = 0.4

[tex]y=\frac{2}{5}[/tex]

Someone please help me out!!

Answers

Answer:

4/ 5

cos A = AB/ AC

= 24/ 30

= 4/ 5

that is option A

A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the current) takes 90 minutes.

Answers

Given :

A motorboat travels 9 miles downstream (with the current) in 30 minutes.

The return trip upstream (against the current) takes 90 minutes.

To Find :

The speed of stream and motorboat.

Solution :

Let, speed of stream is u and speed of motorboat is v.

Now, we know distance is same in both case.

Distance( downstream ) = speed × time

[tex]9 = ( v +u ) \times 0.5\\\\v + u = 18[/tex]....1)

Distance( upstream ) = speed × time

[tex]9 = ( v- u ) \times 1.5\\\\v-u = 6[/tex]....2)

Solving equation 1 and 2 , we get :

v = 12 miles/hour and u = 6 miles/hour

Hence, this is the required solution.

Answer:

The speed of the stream is 6 mph, and the speed of the boat is 12 mph.

Step-by-step explanation:

Downstream:

9 miles in 30 minutes (0.5 hour).

9 mi / 0.5 h = 18 mph

Upstream:

9 miles in 90 minutes (1.5 h).

9 mi / 1.5 h = 6 mph

Let s = speed of stream.

The speed of the stream adds to the speed of the boat downstream and is subtracted fromt he speed of the boat upstream.

Let speed of boat be b.

b + s = 18

b - s = 6

Add the equations.

2b = 24

b = 12

b + s = 18

12 + s = 18

s = 6

The speed of the stream is 6 mph, and the speed of the boat is 12 mph.

easy algebra question below first correct answer gets brainliest

Answers

Answer:

using pythagoras theorem

h^2=p^2+b^2

h^2=12^2+9^2

h^2=144+81

h^2=225

h=[tex]\sqrt{225}[/tex]

h=15

Step-by-step explanation:

what is the surface area? 5cm, 4cm, 6cm, 5cm & 5cm

Answers

Answer:

To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Step-by-step explanation:

SA=2*4*5+2*4*6+2*6*5

=148 cmStep-by-step explanation:

two rational numbers between 2/3 and 5/3​

Answers

Answer:

1.333333333333 or 4/3

1/2x9
step by step please

Answers

[tex]4.5[/tex] ✅

Step-by-step explanation:

[tex] \frac{1}{2} \times 9 \\ = \frac{1 \times 9}{2} \\ = \frac{9}{2} \\ = 4.5[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

so you multiply the numerator which is 1x9= 9
and you leave the denominator alone which will be 9/2 then divide 9*2 which will be 4.5. Hope it makes it easier for you.

V-6<25 what is the answer

Answers

Answer:

v<31

Step-by-step explanation:

Simplify

v-6<25

We want to isolate x.

v<25+6

Simplify

v<31

If this helps please mark as brainliest

An isosceles triangle has base angles that each measure 42°. Which equation can be used to find z, the measure of the third angle of this isosceles triangle in degrees? \

Answers

Answer:

42 + 42 + z = 180

Step-by-step explanation:

Note that:

Base angles in an isosceles triangle are equal in measure.

The sum of angles in a triangle is 180°.

Thus, the equation would be

42 + 42 + z = 180

The first number in a pattern is 8. Each following number is found by subtracting 9 from the previous
number
What is the fifth number in the pattern?

Answers

Answer:

8,-1,-9,-18,-27,-36

and so on i would think it would be -27

Step-by-step explanation:

Answer:

-28

Step-by-step explanation:

other answer off by one

I NEED HELP FAST WILL GIVE BRAINLIEST #1 AND IF YOU CAN #2

Answers

Answer:

Ok

Step-by-step explanation:

So,

Triangle JKL is similar to triangle MNO. Find the measure of side MN. Figures are
not drawn to scale.
L
O
2
J
K
1.4
M
N
0

Answers

Answer:

4.2

Step-by-step explanation:

If they're similar, the fraction between their sides need to be equal, so do this:

2/1.4 = 6/MN

6•1.4/2 = MN

MN = 4.2

simplify
[tex] \sqrt{12} [/tex]

Answers

2 and then on the inside of a square root is 3

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]\huge\boxed{2\sqrt{3}}[/tex]

»»————- ★ ————-««  

Here’s why:  

[tex]\boxed{\text{Simplifying the square root of 12}}\\\\\rightarrow\sqrt{12}\\\\\text{4 can be factored out of 12.}\\\\\rightarrow\sqrt{4(3)}\\\\\text{Two '2's can be factored out of 4.}\\\\\rightarrow\sqrt{2*2*3}\\\\\rightarrow\sqrt{2^2(3)}\\\\\text{Pulling out the terms from under the radical...}\\\\\rightarrow\boxed{2\sqrt{3}}[/tex]

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Hello may any of you help me with these two equations I’m having a little hard time thank you =10 points

Answers

Answer:

a. 10.08

b. 0.0576

please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

Answer:

[tex]1017.9ft ^{3} [/tex]

Step-by-step explanation:

[tex]volume \: of \: cylinder \\ v = \pi \times r {}^{2} \times h \\ = \pi \times 9^2 \times 4 \\ = 1017.9[/tex]

Find the equation of the axis of symmetry of the following parabola algebraically.
y=x^2-12x+34

Answers

i have no idea how to type it out

solve: (x-3)(x+2)=0
answers:
3 and 2
3 and -2
-3 and -2
none of the choices are correct

Answers

Answer:

x=3          x=-2

Step-by-step explanation:

(x-3)(x+2)=0

Using the zero product property

x-3 =0   x+2 =0

x=3          x=-2

Answer:

3 and -2

Step-by-step explanation:

x -3 =0

x= 3

x+2 =0

x= -2

If point D is placed on `bar(AC)`, how will the measure of `/_DAB` relate to the measure of `/_CAB` ?

Answers

Answer:

m`/_DAB` will be equal to m`/_CAB`.

Step-by-step explanation:

Correct on edmentum.

What is the circumference of the circle shown below, given that the length of
AB (the minor arc) is 4?
C
30,
A
A. 48
B. 40
C. 24
d
D. 12

someone pls help no links

Answers

Given:

Length of arc AB is 4 units.

The measure of central angle corresponding to arc AB is 30 degrees.

To find:

The circumference of the circle.

Solution:

The formula for arc length is:

[tex]s=2\pi r\dfrac{\theta }{360^\circ}[/tex]

Where, r is the radius and [tex]\theta[/tex] is the central angle.

It is also written as:

[tex]s=C\dfrac{\theta }{360^\circ}[/tex]

Where, C is the circumference of the circle.

Putting [tex]s=4,\theta =30^\circ[/tex] in the above formula, we get

[tex]4=C\dfrac{30^\circ}{360^\circ}[/tex]

[tex]4=\dfrac{1}{12}C[/tex]

Multiply both sides by 12.

[tex]4\times 12=C[/tex]

[tex]48=C[/tex]

The circumference of the circle is 48 units.

Therefore, the correct option is A.

Find the range of the given data below:
7, 10, 12, 11, 12, 10, 11, 13, 17, 13
Ans: 10​

Answers

Answer:  10

Step-by-step explanation:

Arranged data

7,10,10,11,11,12,12,13,13,17

Range= Highest value - Lowest Vlue

Highest value=17

Lowest value =7

Range=17-7

Range=10

Answer:

[tex]Answer:  10

Step-by-step explanation:

Arranged data

7,10,10,11,11,12,12,13,13,17

Range= Highest value - Lowest Vlue

Highest value=17

Lowest value =7

Range=17-7

Range=10 [/tex]

hope it is helpful to you

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