Question

Find the value of the variable. Round decimal to nearest tenth if necessary. ​

Answer 1

Given:

In a right angle triangle,

Length of legs are x and 7.

Length of hypotenuse = y

Measure of angle between leg 7 and hypotenuse = 33 degrees.

To find:

The value of x and y.

Solution:

In a right angle,

`\tan \theta=(Perpendicular)/(Base)`

`\tan (33^\circ)=(x)/(7)`

`7* \tan (33^\circ)=x`

`7* 0.6494=x`

`4.5458=x`

Approximate the value to the nearest tenth.

`x\approx 4.5`

In a right angle triangle,

`\cos \theta=(Base)/(Hypotenuse)`

`\cos (33^\circ)=(7)/(y)`

`y=(7)/(\cos (33^\circ))`

`y=(7)/(0.83867)`

`y=8.34655`

Approximate the value to the nearest tenth.

`y\approx 8.3`

Therefore, the correct option is D.