What is the surface area of the triangular prism shown?
A.32 square centimeters
B.120 square centimeters
C.184 square centimeters
D.1,560 square centimeters
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Answer:

First don't forget the [ tex ] [ /tex ] in order to execute the latex code.

Step-by-step explanation:

[tex] \sin A=\frac{5}{\sqrt{89}}sinA= 89 [/tex]

[tex] \cos AcosA [/tex] = [tex] \cos [/tex]

The exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is 8√(89)/89

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Given that:

[tex]\sin A=\dfrac{5}{\sqrt{89}}[/tex]

So, from this, we are given the ratio of perpendicular and hypotenuse from the perspective of angle A.

There must be existing a right triangle with same measure of angle A such that:

Perpendicular's length = P = 5 units

and Hypotenuse' length = H = [tex]\sqrt{89}[/tex] units.

Using Pythagoras theorem, we get:

Base' length = B as:

[tex]P^2 + B^2 = H^2\\B = \sqrt{H^2 - P^2}\\\\B = \sqrt{(\sqrt{89})^2 - 5^2}\\\\B = \sqrt{89-25} = \sqrt{64} = 8[/tex]

(took positive root as B is representing length, a non-negative quantity).

Thus, Base is of 8 units length.

Thus, we get:

[tex]\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\cos(A) = \dfrac{B}{H} = \dfrac{8}{\sqrt{89}}[/tex]

Rationalizing, we get:

[tex]\cos(A) = \dfrac{8}{\sqrt{89}} =\dfrac{8}{\sqrt{89}} \times \dfrac{\sqrt{89}}{\sqrt{89}} \\\\\cos(A) = \dfrac{8\sqrt{89}}{89}[/tex]

Thus, the exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is [tex]\dfrac{8\sqrt{89}}{89}[/tex]

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer:(120pi +6 square root 3) msquared

Step-by-step explanation:

9514 1404 393

Answer:

  A

Step-by-step explanation:

A vertical line intersects the graph in more than one place. As a consequence, we say the graph "fails the vertical line test." When the test fails, the graph is not a graph of a function.

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

18+46=64

87.5% of 64=56

64-56=8

56 take the bus

8 dont take the bus

Answer:

10(9u+8q)

Step-by-step explanation:

Step-by-step explanation:

Answer:

answer in the picture

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

x is greater than 2 so all numbers bigger than 2 will be shaded. the circle is open because its not less than or equal to or greater than or equal to.

Answer:

. jsjjsjsjsns jsjikans bjsbbsj. abianan sjsboa kahs hai sbbsjan

bsjsns kskka nanhh aja. sjjab ajj. suhb sjb bsbhshs habaj janab habba

Answer:

I think it its

Step-by-step explanation:

C if its wrong sorry

Answer:

A) y = 0.76x + 3.72

Step-by-step explanation:

Data points: (2, 5) and (11,12)

Slope:

m=(y2-y1)/(x2-x1)

m=(12-5)/(11-2)

m=(7)/9

m= 0.78

Slope-intercept:

y - y1 = m(x - x1)

y - 5 = 0.78(x - 2)

y - 5 = 0.78x - 1.56

y = 0.78x + 3.44

Choice A is the closest to this solution

Answer:

(-9, 9)

Step-by-step explanation:

[tex]6x^{2} +1 = 487[/tex]                                             (Given)

       -1       -1                                     (Getting "x" alone)

[tex]6x^{2} = 486[/tex]                                        (Cont. Getting "x" alone)

÷6      ÷6                                                           ↓

[tex]x^{2} = 81[/tex]                                                              ↓

[tex]\sqrt{x} ^2 = \sqrt{81}[/tex]                           (9 and -9 squared are both equal to 81)

↓             ↓                                                        ↓

x = 9      x = -9                                            (Answer)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

16. 20, 25

17. 3, 4

18. 5, 7

19. 6.5, 5, 3.5, 2, 0.5

Step-by-step explanation:

The way you would solve this is by replacing the variable with an x-value, the answer would be the y-value.

Answer:

∠P=29°

Step-by-step explanation:

The exterior angle theorem says that the exterior angle of a triangle is equal to the sum of the two remote interior angles.

56=∠P+27

∠P=56-27

∠P=29

Answer:

Step-by-step explanation:

(

−

)

(

−

2

+

)

Answer:

Ratio = Width: Height

Ratio = 720 : 540

Cancelling 0

Ratio = 72 : 54

Cancelling by 9

Ratio = 8 : 6

Cancelling be 2

Ratio = 4 : 3

Answer:

-24

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

;0

Answer:

SINCE YOU WROTE ANYTHING ON MINES IM DOING THE SAME  Step-by-step explanation:

Answer: 11/38

Step-by-step explanation: x - y v q r 2÷x029 2%.091 57rq x2 = 11/38

Answer:

T(-3,-2)

Step-by-step explanation:

R(x,y)

R(3,2)

P(6,0)

N(0,-4)

Answer:

First blank is 4.47 and second blank is 4.97

Step-by-step explanation:

It is going up by adding 0.25

Answer:

yes there is two

Step-by-step explanation:

the outlier is the ones that are away from all the others

Answer:

Yes there is

Step-by-step explanation:

There are Many more outliers since the data points are scattered

Answer:

i believe 95 ft ² but I'm not sure sorry

Answer:

95

Step-by-step explanation:

this seems to be a triangular prism. Hopefull this works?

6*1/3 (5+5+5)=95

Answer:

5/9

Step-by-step explanation: