Question

a 9 ft ladder leans against a wall. the base of the ladder is 5 ft from the base of the wall. what is the angle where the ladder meets the ground? round your answer to the nearest whole number. aprils drawing: solve for the unknown value. 56 degrees 54 degrees 55 degrees 53 degrees

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side (distance from base of wall, \(a = 5\) ft) and the hypotenuse (length of ladder, \(h=9\) ft). We use the cosine ratio \(\cos\theta=\frac{a}{h}\).

Step2: Calculate \(\cos\theta\)

Substitute \(a = 5\) and \(h = 9\) into the formula: \(\cos\theta=\frac{5}{9}\approx0.5556\).

Step3: Find the angle \(\theta\)

Take the inverse cosine (arccos) of \(0.5556\): \(\theta=\arccos(0.5556)\). Using a calculator, \(\theta\approx56^{\circ}\).

Answer:

56 degrees