Question

2 a ladder leaning against a wall reaches a height of 16 feet. the ladder itself is 20 feet long. find the angle the ladder makes with the ground

Explanation:

Step1: Identify right triangle sides

The ladder is the hypotenuse ($c=20$ ft), the height is the opposite side to the angle ($o=16$ ft).

Step2: Use sine function for angle

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{16}{20}$

Step3: Simplify the fraction

$\sin(\theta) = \frac{4}{5} = 0.8$

Step4: Calculate inverse sine

$\theta = \arcsin(0.8)$

Answer:

$\theta \approx 53.13^\circ$ (or $0.927$ radians)