Opposite Side Sine Quiz: Find Opposite Side Using Sine

1) Find the opposite side if sin(30°) = opposite/10.

5

6

7

1/8

sin(30°) = 0.5 → 0.5 = opposite/10 → opposite = 10 × 0.5 = 5.

Explanation

sin(30°) = 0.5 → 0.5 = opposite/10 → opposite = 10 × 0.5 = 5.

2) Find the opposite side when angle = 45° and hypotenuse = 14 cm.

10 cm

9.9 cm

12 cm

8 cm

sin(45°) = 0.7071 → opposite = 14 × 0.7071 = 9.9 cm.

Explanation

sin(45°) = 0.7071 → opposite = 14 × 0.7071 = 9.9 cm.

3) To find the opposite side, multiply the sine of the angle by the hypotenuse.

True

False

True. sin(θ) = opposite/hypotenuse → opposite = hypotenuse × sin(θ).

Explanation

True. sin(θ) = opposite/hypotenuse → opposite = hypotenuse × sin(θ).

4) The formula for finding the opposite side is opposite = hypotenuse × ______.

Rearranging sin(θ) = opposite/hypotenuse gives opposite = hypotenuse × sin(θ).

Explanation

Rearranging sin(θ) = opposite/hypotenuse gives opposite = hypotenuse × sin(θ).

Submit

5) Find the opposite side if angle = 60° and hypotenuse = 10 m.

8.66 m

5 m

7 m

9 m

sin(60°) = 0.866 → opposite = 10 × 0.866 = 8.66 m.

Explanation

sin(60°) = 0.866 → opposite = 10 × 0.866 = 8.66 m.

6) A ladder 12 m long makes an angle of 30° with the ground. How high up does it reach?

6 m

8 m

10 m

9 m

sin(30°) = 0.5 → opposite = 12 × 0.5 = 6 m.

Explanation

sin(30°) = 0.5 → opposite = 12 × 0.5 = 6 m.

7) If the hypotenuse increases while the angle remains constant, the opposite side also increases.

True

False

True. opposite = hypotenuse × sin(θ), so increasing hypotenuse increases opposite side proportionally.

Explanation

True. opposite = hypotenuse × sin(θ), so increasing hypotenuse increases opposite side proportionally.

8) Find the opposite side if sin(45°) = opposite/20.

1/12

1/14

1/10

1/16

sin(45°) = 0.7071 → opposite = 20 × 0.7071 = 14.1.

Explanation

sin(45°) = 0.7071 → opposite = 20 × 0.7071 = 14.1.

9) Find the opposite side if hypotenuse = 25 m and angle = 37°.

15 m

16 m

18 m

20 m

sin(37°) = 0.6018 → opposite = 25 × 0.6018 = 15.045 ≈ 15 m.

Explanation

sin(37°) = 0.6018 → opposite = 25 × 0.6018 = 15.045 ≈ 15 m.

10) Select all correct equations for finding the opposite side using sine.

Opposite = hypotenuse × sin(θ)

Sin(θ) = opposite/hypotenuse

Hypotenuse = opposite/sin(θ)

Sin(θ) = hypotenuse/opposite

Cos(θ) = opposite/hypotenuse

sin(θ) = opposite/hypotenuse can be rearranged as opposite = hypotenuse × sin(θ) or hypotenuse = opposite/sin(θ).

Explanation

sin(θ) = opposite/hypotenuse can be rearranged as opposite = hypotenuse × sin(θ) or hypotenuse = opposite/sin(θ).

Submit

11) If angle = 53° and hypotenuse = 10 cm, find the opposite side.

8 cm

7 cm

6 cm

5 cm

sin(53°) = 0.799 → opposite = 10 × 0.799 = 7.99 ≈ 8 cm.

Explanation

sin(53°) = 0.799 → opposite = 10 × 0.799 = 7.99 ≈ 8 cm.

12) The sine ratio compares the opposite side to the adjacent side.

True

False

False. The sine ratio compares the opposite side to the hypotenuse.

Explanation

False. The sine ratio compares the opposite side to the hypotenuse.

Submit

14) Find the opposite side if angle = 20° and hypotenuse = 15 m.

5.13 m

6.84 m

4.5 m

7 m

sin(20°) = 0.3420 → opposite = 15 × 0.3420 = 5.13 m.

Explanation

sin(20°) = 0.3420 → opposite = 15 × 0.3420 = 5.13 m.

15) If sin(θ) = 0.8 and hypotenuse = 25 m, find the opposite side.

18 m

20 m

19.5 m

25 m

opposite = 25 × 0.8 = 20 m.

Explanation

opposite = 25 × 0.8 = 20 m.

16) The opposite side is always shorter than the hypotenuse.

True

False

True. Since sin(θ) ≤ 1, opposite = hypotenuse × sin(θ) will always be less than hypotenuse.

Explanation

True. Since sin(θ) ≤ 1, opposite = hypotenuse × sin(θ) will always be less than hypotenuse.

17) Find the opposite side if angle = 75° and hypotenuse = 8 cm.

7.7 cm

8 cm

6 cm

7 cm

sin(75°) = 0.9659 → opposite = 8 × 0.9659 = 7.73 cm ≈ 7.7 cm.

Explanation

sin(75°) = 0.9659 → opposite = 8 × 0.9659 = 7.73 cm ≈ 7.7 cm.

18) Select all statements that are true about using sine to find the opposite side.

You must know the hypotenuse

Sine uses the ratio of opposite to hypotenuse

It works only for right triangles

It can find adjacent side directly

Sine = hypotenuse/opposite

Sine applies only to right triangles and relates opposite side to hypotenuse.

Explanation

Sine applies only to right triangles and relates opposite side to hypotenuse.

Submit

19) Find the opposite side if angle = 10° and hypotenuse = 30 m.

5.2 m

4.8 m

6 m

3 m

sin(10°) = 0.1736 → opposite = 30 × 0.1736 = 5.208 ≈ 5.2 m.

Explanation

sin(10°) = 0.1736 → opposite = 30 × 0.1736 = 5.208 ≈ 5.2 m.

20) If angle = 80° and hypotenuse = 50 m, find the opposite side.

49.2 m

48.9 m

50 m

47 m

sin(80°) = 0.9848 → opposite = 50 × 0.9848 = 49.24 m ≈ 49.2 m.

Explanation

sin(80°) = 0.9848 → opposite = 50 × 0.9848 = 49.24 m ≈ 49.2 m.

Opposite Side Sine Quiz: Find Opposite Side Using Sine

1) Find the opposite side if sin(30°) = opposite/10.

2)

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

2) Find the opposite side when angle = 45° and hypotenuse = 14 cm.

3) To find the opposite side, multiply the sine of the angle by the hypotenuse.

4) The formula for finding the opposite side is opposite = hypotenuse × ______.

5) Find the opposite side if angle = 60° and hypotenuse = 10 m.

6) A ladder 12 m long makes an angle of 30° with the ground. How high up does it reach?

7) If the hypotenuse increases while the angle remains constant, the opposite side also increases.

8) Find the opposite side if sin(45°) = opposite/20.

9) Find the opposite side if hypotenuse = 25 m and angle = 37°.

10) Select all correct equations for finding the opposite side using sine.

11) If angle = 53° and hypotenuse = 10 cm, find the opposite side.

12) The sine ratio compares the opposite side to the adjacent side.

13) In a right triangle, sin(θ) equals the ratio of the ______ to the hypotenuse.

14) Find the opposite side if angle = 20° and hypotenuse = 15 m.

15) If sin(θ) = 0.8 and hypotenuse = 25 m, find the opposite side.

16) The opposite side is always shorter than the hypotenuse.

17) Find the opposite side if angle = 75° and hypotenuse = 8 cm.

18) Select all statements that are true about using sine to find the opposite side.

19) Find the opposite side if angle = 10° and hypotenuse = 30 m.

20) If angle = 80° and hypotenuse = 50 m, find the opposite side.