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

Answer: 20√3 cm

Question 2: In triangle XYZ, angle X is 45°, and side XY (opposite to angle X) is 14√2 cm. Find the length of side XZ, the hypotenuse. Use SOH.

Answer: 28 cm

Question 3: A ladder leaning against a wall makes a 60° angle with the ground. The ladder's foot is 8 meters from the wall. Calculate the length of the ladder.

Answer: 16 meters

Question 4: Construct a right-angled triangle where the side opposite to a 45° angle measures 7.07 cm. Use SOH to determine the length of the hypotenuse.

Answer: 10 cm

Question 5: A tree casts a shadow 12 meters long when the sun is at an angle of elevation of 30°. Calculate the height of the tree using SOH.

Answer: 6.93 meters

Question 6: A pilot sights a distant tower at an angle of 25°. The helicopter is 150 meters above ground level. Calculate the horizontal distance from the helicopter to the tower using SOH.

Answer: 338.7 meters

Question 7: A ramp makes an angle of 15° with the ground. The top of the ramp is 5 meters above the ground. Calculate the length of the ramp using SOH.

Answer: 19.3 meters

Question 8: Explain the mistake in the following calculation: A student calculates the height of a tree as 10 meters using sin(30°) = opposite/hypotenuse, with hypotenuse 20 meters, but uses sin(30°)=1/3. Identify and correct the error.

Answer: They incorrectly used sin(30°)=1/3 instead of 1/2. Correct calculation: height = 20 × sin(30°) = 20 × 1/2 = 10 meters.

Question 9: A right-angled triangle has an angle of 60° and the side opposite this angle is 15 cm. Use SOH to find the length of the hypotenuse.

Answer: 30 cm

Question 10: Find the missing side in a right triangle where the hypotenuse is 25 cm and the angle opposite the missing side is 45°. Use SOH.

Answer: 17.68 cm

Question 11: A building's height is estimated using a theodolite at an angle of 40°, with a distance of 120 meters from the building. Calculate the height of the building using SOH.

Answer: 93.1 meters

Question 12: Identify the common mistake made when students confuse sine and cosine in SOH calculations, and explain how to avoid it.

Answer: Students often mix up sine and cosine; sine is for opposite/hypotenuse, cosine is for adjacent/hypotenuse. To avoid, remember SOH only involves sine and opposite side.