Question

on your own: applications of right triangle
on your own
applications of right triangle trigonometry
now it’s time to practice on your own
at a certain time of the day, the angle of elevation of the sun is 18.5°.
what is the length of the shadow cast by your friend, who is 1.75 m tall?
round your answer to the nearest tenth of a meter.
enter your answer in the box.

Explanation:

Step1: Define trigonometric relationship

The friend's height is the opposite side, shadow length is the adjacent side to the elevation angle. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Rearrange for shadow length

Let $x$ = shadow length. Solve for $x$:
$x = \frac{1.75}{\tan(18.5^\circ)}$

Step3: Calculate the value

First compute $\tan(18.5^\circ) \approx 0.3346$, then:
$x \approx \frac{1.75}{0.3346} \approx 5.2$

Answer:

5.2 meters