Question

15. Given the right triangle in the diagram below,
what is the value of x, to the nearest foot?
A. 11
B. 17
c. 18
D. 22

Answer 1

Answer:

The answer to your question is 18 feet

Step-by-step explanation:

Data

hypotenuse = x

angle = 40°

adjacent side = 14 ft

Process

1.- To solve this problem we use trigonometric functions. The trigonometric function that relates the adjacent side and the hypotenuse is cosine.

            cos Ф  = $\frac{adjacent side}{hypotenuse}$

Solve for hypotenuse

             hypotenuse = $\frac{adjacent side}{cos\alpha }$

2.- Substitution

              hypotenuse = $\frac{14}{cos 40}$

3.- Simplification

               hypotenuse = $\frac{14}{0.766}$

4.- Result

               hypotenuse = x = 18.27 ≈ 18 ft

Answer 2

The value of x in the right triangle is 18 ft

Right angle triangle:

Right angle triangle have one of its angles as 90 degrees. The sides can be found using trigonometric ratios. Therefore, let's find x

cos 40° = adjacent / hypotenuse

cos 40° = 14 / x

cross multiply

x cos 40° = 14

x = 14 / cos 40°

x = 14 / 0.76604444311

x = 18.2767624021

x = 18 ft

The value of x in the triangle is 18 ft.

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