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: Identify the trigonometric relation

We know the length of the ladder (hypotenuse $c = 25$ feet) and the angle $\theta=18^{\circ}$ between the ladder and the wall. We want to find the adjacent - side $x$ (height up the wall) to the angle $\theta$. We use the cosine function $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos\theta=\frac{x}{c}$

Step2: Substitute the values

Substitute $\theta = 18^{\circ}$ and $c = 25$ into the formula $\cos\theta=\frac{x}{c}$. So $x = c\times\cos\theta$.
$x=25\times\cos(18^{\circ})$

Step3: Calculate the value

We know that $\cos(18^{\circ})\approx0.9511$. Then $x = 25\times0.9511=23.7775\approx23.8$ feet.

Answer:

23.8 ft