Question 1: Given a right-angled triangle where the adjacent side is 7 cm and the angle is 45°, calculate the length of the hypotenuse.

Answer: 9.9

Question 2: In a right triangle, the adjacent side is 10 units and the hypotenuse is 13 units. Find the measure of the angle adjacent to the side of length 10.

Answer: 51.8°

Question 3: A ladder leaning against a wall makes a 60° angle with the ground. If the ladder is 8 meters long, find the distance from the foot of the ladder to the wall.

Answer: 4.62

Question 4: Construct a right-angled triangle where the hypotenuse is 12 cm and the angle adjacent to the side of length 9 cm. Show the calculation for the other side.

Answer: 8.4

Question 5: A ramp rises 3 meters vertically over a horizontal distance of 5 meters. Using CAH, find the angle of the incline.

Answer: 30.96°

Question 6: A satellite dish has an angle of elevation of 45°. The dish's arm is 15 meters long. Calculate the height from the ground to the satellite (along the dish's line).

Answer: 10.6

Question 7: A staircase makes a 35° angle with the ground. If the staircase is 4 meters long, calculate the vertical height of the staircase.

Answer: 2.3

Question 8: In a right triangle, the adjacent side is 8 units and the hypotenuse is 10 units. What is the value of the angle adjacent to the side of length 8?

Answer: 53.13°

Question 9: Identify the common mistake made when students confuse sine and cosine in CAH calculations and describe how to correct it.

Answer: Confusing sine with cosine; students should remember CAH focuses on cosine for adjacent/hypotenuse ratio.

Question 10: A tree casts a shadow 12 meters long when the sun is at an angle of 70°. Use CAH to estimate the height of the tree.

Answer: 40.4

Question 11: A lighthouse is 50 meters tall. From a point 30 meters away from its base, the angle of elevation to the top is 60°. Verify the height using CAH.

Answer: 50.0