Question 1: Calculate the length of the adjacent side when the hypotenuse is 10 units and the angle is 60° using CAH.

Answer: 5

Question 2: In a right triangle, if the hypotenuse is 15 units and the angle is 45°, find the adjacent side length.

Answer: 10.61

Question 3: A ladder leans against a wall, forming a 75° angle with the ground. If the ladder's length is 12 meters, find the length of the adjacent side (distance from base to wall).

Answer: 3.1

Question 4: A surveyor measures an angle of 50° between a line of sight and the ground. If the adjacent side is 20 meters, what is the hypotenuse length?

Answer: 25.98

Question 5: Construct a right triangle where the hypotenuse is 13 units and the adjacent side is 5 units. Label the angle θ at the origin, showing the application of CAH.

Answer: Student draws triangle with specified sides, labels θ where cos θ = 5/13

Question 6: Using CAH, find the hypotenuse when the adjacent side is 8 units and the angle is 30°.

Answer: 16

Question 7: A shadow cast by a tower is 25 meters long when the angle of elevation to the top of the tower is 75°. Using CAH, find the height of the tower.

Answer: 97

Question 8: A person walks 30 meters directly away from a building. The angle of depression to the top of the building is 60°. Find the height of the building using CAH.

Answer: 17.32

Question 9: A drone flies 20 meters horizontally from a point where it observes a tower at a 45° angle. Find the height of the tower using CAH.

Answer: 20

Question 10: Error Analysis: A student calculates cos 45° as 0.50 instead of the correct value. Identify and explain the mistake, then correct it.

Answer: Mistake: Incorrect value for cos 45°. Correct value: 0.707. The student may have used approximation or misremembered, but cos 45° = 1/√2 ≈ 0.707.

Question 11: Challenge: In a right triangle, the adjacent side is 9 units and the hypotenuse is 15 units. Find the angle θ using CAH, and justify your answer with calculations.

Answer: θ ≈ 36.87°