Question 1: Calculate the length of side AB in a right-angled triangle where the hypotenuse AC is 10 cm and the angle at A is 30°. Use CAH.

Answer: 5√3 cm

Question 2: In a right triangle, the side opposite the 45° angle is 7.07 cm. Find the adjacent side using CAH.

Answer: 7.07 cm

Question 3: A ladder leans against a wall, forming a 60° angle with the ground. If the ladder's length is 12 meters, find the distance from the wall to the base of the ladder using CAH.

Answer: 6 meters

Question 4: Using CAH, find the length of the side adjacent to a 50° angle if the hypotenuse is 15 cm.

Answer: 11.49 cm

Question 5: A right triangle has an angle of 35° and the side opposite this angle measures 8 cm. Calculate the length of the hypotenuse using CAH.

Answer: 9.83 cm

Question 6: Problem Solving: A ramp makes a 25° angle with the ground. If the ramp's length is 20 meters, what is the horizontal distance from the start of the ramp to the bottom? Use CAH.

Answer: 18.10 meters

Question 7: A tree casts a shadow 12 meters long when the sun's altitude angle is 45°. Find the height of the tree using CAH.

Answer: 12√2 meters

Question 8: Construct a right-angled triangle with hypotenuse 13 cm and an angle of 40°, then label the sides. Use CAH to find the length of the side adjacent to the 40° angle.

Answer: 9.94 cm

Question 9: Challenge: A drone flies 80 meters horizontally and makes a 60° angle to the ground. Find the approximate length of the drone's path using CAH.

Answer: 92.38 meters

Question 10: Error Analysis: A student calculates the adjacent side as 10 cm when given a hypotenuse of 13 cm and an angle of 50°, but forgets to check the cosine value. Identify the mistake and correct it.

Answer: Their calculation used the sine instead of cosine; the correct adjacent side is 13×cos50° ≈ 8.39 cm.