Question

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: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse (\(c = 25\) ft) and the height on the wall (\(a\)) is adjacent to the given angle (\(\theta=18^{\circ}\)). We use the cosine function: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos(18^{\circ})=\frac{a}{25}\).

Step2: Solve for \(a\)

Rearrange the formula to \(a = 25\times\cos(18^{\circ})\).
Using a calculator, \(\cos(18^{\circ})\approx0.9510565163\).
Then \(a = 25\times0.9510565163\approx23.8\) ft.

Answer:

23.8 ft