1. **Problem:** A 20-ft ladder is leaning against a wall making a 62° angle with the floor. Find the distance from the base of the ladder to the wall. 2. **Formula:** Use the cosine function because the adjacent side (distance from wall) and hypotenuse (ladder length) are involved. $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply values:** $$\cos(62^\circ) = \frac{\text{distance}}{20}$$ 4. **Solve for distance:** $$\text{distance} = 20 \times \cos(62^\circ)$$ 5. **Calculate:** $$\cos(62^\circ) \approx 0.4695$$ $$\text{distance} = 20 \times 0.4695 = 9.39$$ 6. **Answer:** The base of the ladder is approximately **9.39 ft** from the wall. 1. **Problem:** A 20-ft ladder is leaning against a wall making a 78° angle with the floor. Find the height of the top of the ladder from the ground. 2. **Formula:** Use the sine function because the opposite side (height) and hypotenuse (ladder length) are involved. $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply values:** $$\sin(78^\circ) = \frac{\text{height}}{20}$$ 4. **Solve for height:** $$\text{height} = 20 \times \sin(78^\circ)$$ 5. **Calculate:** $$\sin(78^\circ) \approx 0.9781$$ $$\text{height} = 20 \times 0.9781 = 19.56$$ 6. **Answer:** The top of the ladder is approximately **19.56 ft** from the ground.