Question 1: Calculate the length of side AB in a right-angled triangle where angle C is 30°, and side AC (adjacent to angle C) measures 10 cm. Use SOH.

Answer: 20√3

Question 2: In a right triangle, the hypotenuse is 15 cm and the angle opposite side BC is 45°. Find the length of side BC. (Use SOH).

Answer: 15 / √2

Question 3: Construct a right-angled triangle where the side opposite 60° is 12 cm. Calculate the length of the hypotenuse.

Answer: 24

Question 4: A ladder leans against a wall, making a 50° angle with the ground. If the ladder is 8 meters long, find the height it reaches on the wall.

Answer: 8 × sin(50°)

Question 5: A tree casts a shadow 6 meters long when the Sun's angle of elevation is 40°. How tall is the tree?

Answer: 6 / tan(40°)

Question 6: Calculate the length of side AC in a right triangle where angle B is 45°, and side AB (adjacent to B) is 8 cm.

Answer: 8

Question 7: A helicopter climbs at a 30° angle to the ground. If the vertical height gained is 150 meters, find the horizontal distance traveled.

Answer: 150 / tan(30°)

Question 8: A right triangle has sides of lengths 7 and 24. Find the length of the hypotenuse, assuming the 7-unit side is opposite to a 20° angle. Use SOH.

Answer: 24

Question 9: Identify the mistake: A student finds side AB as 10 cm knowing angle C is 45° and side AC (adjacent to C) is 7 cm, using SOH. The student says the hypotenuse is 7√2 cm. Correct or incorrect? Explain.

Answer: Incorrect; hypotenuse = 7 / cos(45°) = 7√2, but if using SOH, it should be based on sine or cosine, not tangent.

Question 10: Challenge: In a right triangle, the hypotenuse is 20 cm and the angle opposite side BC is 60°. Find the length of side BC and side AC.

Answer: BC = 20 × sin(60°) = 10√3; AC = 20 × cos(60°) = 10