SOHCAHTOA Ladder Quiz: Ladder Against Wall Scenario (SOHCAHTOA Method)

1) A 10 m ladder leans against a wall at an angle of 60°. How high does it reach?

8.66 m

6 m

7.5 m

9 m

Height = Ladder × sin(angle) = 10 × sin(60°) = 10 × 0.866 = 8.66 m.

Explanation

Height = Ladder × sin(angle) = 10 × sin(60°) = 10 × 0.866 = 8.66 m.

2) A 12 m ladder makes a 45° angle with the ground. How high up the wall does it touch?

8.5 m

9 m

8.49 m

10 m

Height = 12 × sin(45°) = 12 × 0.7071 = 8.49 m.

Explanation

Height = 12 × sin(45°) = 12 × 0.7071 = 8.49 m.

3) If a ladder makes a 90° angle with the ground, it is fully vertical.

True

False

True. At 90°, sin(90°) = 1, so height = ladder length. The ladder is perfectly upright.

Explanation

True. At 90°, sin(90°) = 1, so height = ladder length. The ladder is perfectly upright.

4) To find how high a ladder reaches, multiply the ladder length by the ______ of the angle it makes with the ground.

Height is found using sine, since sin(θ) = Opposite/Hypotenuse, and the opposite side is the wall height.

Explanation

Height is found using sine, since sin(θ) = Opposite/Hypotenuse, and the opposite side is the wall height.

Submit

5) A 15 ft ladder makes an angle of 30° with the ground. How high does it reach?

7.5 ft

10 ft

12 ft

15 ft

Height = 15 × sin(30°) = 15 × 0.5 = 7.5 ft.

Explanation

Height = 15 × sin(30°) = 15 × 0.5 = 7.5 ft.

6) A smaller angle with the ground means the ladder reaches higher up the wall.

True

False

False. As angle decreases, sin(θ) decreases, so the ladder reaches less height.

Explanation

False. As angle decreases, sin(θ) decreases, so the ladder reaches less height.

7) If a 20 ft ladder reaches 17.32 ft up the wall, what angle does it make with the ground?

60°

45°

30°

75°

sin(θ) = 17.32/20 = 0.866 → θ = sin⁻¹(0.866) = 60°.

Explanation

sin(θ) = 17.32/20 = 0.866 → θ = sin⁻¹(0.866) = 60°.

Submit

9) A 25 m ladder leans at 53°. What is the height reached?

20 m

15 m

25 m

21 m

Height = 25 × sin(53°) = 25 × 0.799 = 19.98 ≈ 20 m.

Explanation

Height = 25 × sin(53°) = 25 × 0.799 = 19.98 ≈ 20 m.

10) If the angle increases while ladder length stays same, what happens to the height?

Increases

Decreases

Stays same

Becomes zero

Height increases as sin(θ) increases with angle, reaching maximum at 90°.

Explanation

Height increases as sin(θ) increases with angle, reaching maximum at 90°.

11) At 0°, a ladder lies flat on the ground and reaches no height.

True

False

True. sin(0°) = 0, so height = 0.

Explanation

True. sin(0°) = 0, so height = 0.

12) A ladder 8 m long makes an angle of 37° with the ground. Find the height.

4.5 m

5 m

6 m

7 m

Height = 8 × sin(37°) = 8 × 0.6018 = 4.81 ≈ 5 m.

Explanation

Height = 8 × sin(37°) = 8 × 0.6018 = 4.81 ≈ 5 m.

13) If a 10 m ladder reaches 5 m high, what is the angle made with the ground?

30°

45°

60°

25°

sin(θ) = 5/10 = 0.5 → θ = sin⁻¹(0.5) = 30°.

Explanation

sin(θ) = 5/10 = 0.5 → θ = sin⁻¹(0.5) = 30°.

14) Select all correct formulas for finding the height the ladder reaches.

Height = Ladder × sin(θ)

Height = Ladder × cos(θ)

Height = Opposite × sin(θ)

Height = Hypotenuse × sin(θ)

Height = sin(θ) / Ladder

Height = Hypotenuse × sin(θ). The ladder is the hypotenuse in this case.

Explanation

Height = Hypotenuse × sin(θ). The ladder is the hypotenuse in this case.

Submit

15) A 10 m ladder leans at 75°. How high up the wall does it reach?

9.66 m

8.5 m

7.5 m

9 m

Height = 10 × sin(75°) = 10 × 0.9659 = 9.66 m.

Explanation

Height = 10 × sin(75°) = 10 × 0.9659 = 9.66 m.

16) If two ladders have same angle but different lengths, the longer ladder will reach higher.

True

False

True. Height = Ladder × sin(θ). Increasing ladder increases height proportionally.

Explanation

True. Height = Ladder × sin(θ). Increasing ladder increases height proportionally.

17) If ladder = 10 m and angle = 0°, height =

0 m

5 m

10 m

Infinite

Height = 10 × sin(0°) = 10 × 0 = 0 m. Ladder lies flat.

Explanation

Height = 10 × sin(0°) = 10 × 0 = 0 m. Ladder lies flat.

18) When angle increases, the sine value ______.

As angle increases from 0° to 90°, sine increases from 0 to 1, so height increases.

Explanation

As angle increases from 0° to 90°, sine increases from 0 to 1, so height increases.

Submit

19) A 13 ft ladder reaches 12 ft up. What is the angle made with the ground?

67.4°

70°

75°

60°

sin(θ) = 12/13 = 0.923 → θ = sin⁻¹(0.923) ≈ 67.38°. The closest precise answer is 67.4°.

Explanation

sin(θ) = 12/13 = 0.923 → θ = sin⁻¹(0.923) ≈ 67.38°. The closest precise answer is 67.4°.

20) Select all scenarios where the ladder reaches 8.66 m high.

Ladder = 10 m, angle = 60°

Ladder = 15 m, angle = 30°

Ladder = 20 m, angle = 30°

Ladder = 10 m, angle = 30°

Ladder = 5 m, angle = 60°

Height = Ladder × sin(angle). For A: 10×0.866=8.66 (correct). For E: 5×0.866=4.33 (incorrect). Only A gives 8.66 m.

Explanation

Height = Ladder × sin(angle). For A: 10×0.866=8.66 (correct). For E: 5×0.866=4.33 (incorrect). Only A gives 8.66 m.

SOHCAHTOA Ladder Quiz: Ladder Against Wall Scenario (SOHCAHTOA Method)

1) A 10 m ladder leans against a wall at an angle of 60°. How high does it reach?

2)

What first name or nickname would you like us to use?

2) A 12 m ladder makes a 45° angle with the ground. How high up the wall does it touch?

3) If a ladder makes a 90° angle with the ground, it is fully vertical.

4) To find how high a ladder reaches, multiply the ladder length by the ______ of the angle it makes with the ground.

5) A 15 ft ladder makes an angle of 30° with the ground. How high does it reach?

6) A smaller angle with the ground means the ladder reaches higher up the wall.

7) If a 20 ft ladder reaches 17.32 ft up the wall, what angle does it make with the ground?

8) If sin(θ) = height / ladder, then height = ladder × ______.

9) A 25 m ladder leans at 53°. What is the height reached?

10) If the angle increases while ladder length stays same, what happens to the height?

11) At 0°, a ladder lies flat on the ground and reaches no height.

12) A ladder 8 m long makes an angle of 37° with the ground. Find the height.

13) If a 10 m ladder reaches 5 m high, what is the angle made with the ground?

14) Select all correct formulas for finding the height the ladder reaches.

15) A 10 m ladder leans at 75°. How high up the wall does it reach?

16) If two ladders have same angle but different lengths, the longer ladder will reach higher.

17) If ladder = 10 m and angle = 0°, height =

18) When angle increases, the sine value ______.

19) A 13 ft ladder reaches 12 ft up. What is the angle made with the ground?

20) Select all scenarios where the ladder reaches 8.66 m high.