Question

a ladder with a length of 24 feet is leaning against a wall. the angle formed by the base of the ladder and the ground measures 50°. how far is the base of the ladder from the wall? 28.6 feet 37.3 feet 15.4 feet 18.4 feet

Explanation:

Step1: Identify the trigonometric function

We have a right - triangle where the length of the ladder is the hypotenuse (\(c = 24\) feet) and we want to find the adjacent side (\(x\)) to the given angle (\(\theta=50^{\circ}\)). We use the cosine function: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(x = c\times\cos\theta\).

Step2: Substitute the values

Substitute \(c = 24\) and \(\theta = 50^{\circ}\) into the formula. We know that \(\cos(50^{\circ})\approx0.6428\). Then \(x=24\times\cos(50^{\circ})\).

$$x = 24\times0.6428=15.4272\approx15.4$$

Answer:

15.4 feet