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 ratio

We know the length of the hypotenuse (ladder length \(c = 25\) ft) and we need to find the adjacent side (\(x\)) to the given angle \(\theta=18^{\circ}\). We use the cosine ratio \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(x = c\times\cos\theta\).

Step2: Substitute the values

Substitute \(c = 25\) and \(\theta = 18^{\circ}\) into the formula. \(\cos(18^{\circ})\approx0.9511\). Then \(x=25\times\cos(18^{\circ})\).

$$x = 25\times0.9511=23.7775$$

Step3: Round the result

Round \(23.7775\) to the nearest tenth. Since the hundredth - digit is \(7\gt5\), we round up the tenth - digit. So \(23.7775\approx23.8\)

Answer:

23.8 ft