Question 1: Calculate the length of the side opposite the 30° angle in a right triangle where the adjacent side is 10 cm, using TOA.

Answer: 5

Question 2: In a right triangle, the angle is 45°, and the adjacent side is 8 cm. Find the opposite side using TOA.

Answer: 8

Question 3: Construct a right triangle where the opposite side is 6 cm, the angle between the hypotenuse and adjacent side is 60°. Draw on the grid.

Answer: Draw a right triangle with the specified dimensions, showing the 60° angle.

Question 4: A ladder leans against a wall, forming a 75° angle with the ground. The foot of the ladder is 4 meters from the wall. Use TOA to find the height the ladder reaches on the wall.

Answer: 15.5

Question 5: A tree casts a shadow 12 meters long when the sun’s elevation angle is 30°. Using TOA, find the height of the tree.

Answer: 6

Question 6: A person looks at the top of a building and measures the angle of elevation as 50°. If the person is standing 30 meters from the building, find the height of the building.

Answer: 42.4

Question 7: A ramp makes a 25° angle with the ground. The ramp is 8 meters long. Use TOA to determine how high the ramp reaches.

Answer: 3.4

Question 8: In a right triangle, the tangent of an angle is 0.5. The adjacent side is 5 cm. Calculate the length of the opposite side.

Answer: 2.5

Question 9: A kite flying at a height of 20 meters is observed from a point 30 meters away from the kite's base. Find the angle of elevation to the kite using TOA.

Answer: 34.5

Question 10: Common mistake: A student calculates  using sine instead of tangent when solving for the height of a building. Identify and explain the mistake.

Answer: Using sine relates opposite and hypotenuse, but for height and distance, tangent (opposite/adjacent) is needed.