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 ladder is leaning against a building, forming a 70° angle with the ground. the base of the ladder is 8.2 ft from the base of the building.
what is the length of the ladder?
round your answer to the nearest foot.
enter your answer in the box.

Explanation:

Step1: Identify trigonometric ratio

We know the adjacent side to the $70^\circ$ angle ($8.2$ ft) and need the hypotenuse (ladder length $L$). Use cosine: $\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute known values

$\cos(70^\circ) = \frac{8.2}{L}$

Step3: Solve for $L$

Rearrange to isolate $L$: $L = \frac{8.2}{\cos(70^\circ)}$
Calculate $\cos(70^\circ) \approx 0.3420$, so $L \approx \frac{8.2}{0.3420}$

Step4: Compute and round

$L \approx 23.98$, round to nearest foot.

Answer:

24 ft