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,

$\tan \theta=\dfrac{Perpendicular}{Base}$

$\tan (33^\circ)=\dfrac{x}{7}$

$7\times \tan (33^\circ)=x$

$7\times 0.6494=x$

$4.5458=x$

Approximate the value to the nearest tenth.

$x\approx 4.5$

In a right angle triangle,

$\cos \theta=\dfrac{Base}{Hypotenuse}$

$\cos (33^\circ)=\dfrac{7}{y}$

$y=\dfrac{7}{\cos (33^\circ)}$

$y=\dfrac{7}{0.83867}$

$y=8.34655$

Approximate the value to the nearest tenth.

$y\approx 8.3$

Therefore, the correct option is D.