Question

on your own: applications of right triangle trigonometry
on your own
applications of right triangle trigonometry
now it’s time to practice on your own
a vertical tower of a bridge has a cable attached to it 24 m above the ground. the other end of the cable is secured on the ground so that the cable is pulled tight. the angle between the cable and the tower is 63°.
what is the approximate length of the cable?
round your answer to the nearest tenth of a meter.
enter your answer in the box.

Explanation:

Step1: Identify adjacent side, angle

We have a right triangle where:

• Adjacent side to the 63° angle (tower height) = $24$ m
• The cable is the hypotenuse $L$, which we need to find.
• Use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Rearrange to solve for $L$

$$\cos(63^\circ) = \frac{24}{L}$$
Rearrange to isolate $L$:
$$L = \frac{24}{\cos(63^\circ)}$$

Step3: Calculate the value

First, $\cos(63^\circ) \approx 0.4540$
$$L \approx \frac{24}{0.4540} \approx 52.9$$

Answer:

$52.9$ meters