Question

solving problems using trigonometric ratios
a 25 - foot long ladder is propped against a wall at an angle of 18° with the wall. how high up the wall does the ladder reach? round the answer to the nearest tenth of a foot.
13.8 ft
23.8 ft
26.3 ft
80.9 ft

Explanation:

Step1: Define cosine relationship

We use the cosine function, where $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 18^\circ$, the hypotenuse is the ladder length (25 ft), and the adjacent side is the height $h$ up the wall.

Step2: Rearrange to solve for $h$

Rearrange the formula to isolate $h$: $h = 25 \times \cos(18^\circ)$

Step3: Calculate the value

First, find $\cos(18^\circ) \approx 0.9511$. Then compute $h \approx 25 \times 0.9511 = 23.7775$

Step4: Round to nearest tenth

Round 23.7775 to the nearest tenth: $23.8$

Answer:

B. 23.8 ft