Grade 11 Math: Sine Ratio Worksheet
Explore the sine ratio in right-angled triangles, including calculating sine values, finding missing sides and angles, and applying the sine ratio in problem-solving.
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Grade 11 Math: Sine Ratio
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Read each question carefully and answer to the best of your ability. Show all your work for full credit. Round your answers to two decimal places where appropriate.
1. In a right-angled triangle, the sine of an angle is defined as the ratio of which two sides?
Adjacent / Hypotenuse
Opposite / Hypotenuse
Opposite / Adjacent
Hypotenuse / Opposite
2. If sin(θ) = 0.5, what is the approximate value of θ in degrees?
30°
45°
60°
90°
3. The sine ratio is only applicable to triangles.
4. In a right-angled triangle, the side opposite the right angle is called the .
5. The value of sin(90°) is .
6. For the right-angled triangle shown below, find sin(A) and sin(B). Round your answers to two decimal places.
sin(A) =
sin(B) =
7. In a right-angled triangle, if the hypotenuse is 10 cm and one angle is 30°, find the length of the side opposite the 30° angle. Round your answer to two decimal places.
8. A ladder 8 meters long leans against a wall, making an angle of 65° with the ground. How high up the wall does the ladder reach? Round your answer to two decimal places.
9. In a right-angled triangle, the side opposite an angle is 7 units long, and the hypotenuse is 12 units long. Find the measure of the angle. Round your answer to one decimal place.
10. A kite string is 50 meters long and makes an angle of 55° with the ground. Assuming the string is taut, what is the height of the kite above the ground? Round your answer to two decimal places.