Question

Find the value of x. Round the length to the nearest tenth. Diagram is not drawn to scale.

A.7.2ft
B.6.9ft
C.13.9ft
D.9.7ft

Answer 1

Answer: A. 7.2 ft

Explanation:

Given: A right triangle with hypotenuse 10 ft and base angle
`44^(\circ)`

By using Trigonometry, we have

`\cos (44^(\circ))=\frac{\text{side adjacent to }44^(\circ)}{\text{hypotenuse}}\\\\\Rightarrow \cos (44^(\circ))=(x)/(10)\\\\\Rightarrow0.71933980033=(x)/(10)\\\\\Rightarrow\ x=10*0.71933980033=7.1933980033\approx7.2\ ft.`

Hence, the value of x = 7.2 ft.

Answer 2

(A)
`x=7.2 ft`

Explanation:

Given: A triangle whose base angle is 44° and hypotenuse is 10ft.

To find: The value of x.

solution: Using the trigonometry, we have

`(x)/(10)=cos44^{{\circ}}`

⇒
`x=10{*}cos44^{{\circ}}`

⇒
`x=10{*}0.72`

⇒
`x=7.2 ft`

Thus,the value of
`x=7.2 ft`