Sine Ratio (SOH)

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Show your work for each problem.

1.
In a right triangle, the sine of an angle equals:
1. a)Hypotenuse / Opposite
2. b)Opposite / Hypotenuse
3. c)Opposite / Adjacent
4. d)Adjacent / Hypotenuse
2.
What is ?
1. a)
2. b)
3. c)
4. d)
3.
What is ?
4.
In a right triangle, the opposite side is and the hypotenuse is . What is ?
5.
What is ?
1. a)
2. b)
3. c)
4. d)
6.
A ladder is meters long and makes a angle with the ground. How high does it reach on the wall? (Round to 2 decimal places)
7.
A rope attached to the top of a meter pole makes a angle with the ground. How long is the rope? (Use sin(50°) ≈ 0.766)
8.
An airplane climbs at a angle. After traveling meters along its flight path, how much altitude has it gained? (Use sin(20°) ≈ 0.342)
9.
Which formula would you use to find the hypotenuse when you know the opposite side and the angle?
1. a)hypotenuse = opposite + sin(θ)
2. b)hypotenuse = sin(θ) ÷ opposite
3. c)hypotenuse = opposite × sin(θ)
4. d)hypotenuse = opposite ÷ sin(θ)
10.
A ramp has a height of meters and a length (hypotenuse) of meters. What angle does the ramp make with the ground? (Round to the nearest degree)
11.
A kite string is meters long and makes a angle with the ground. How high is the kite flying? (Use sin(35°) ≈ 0.574, round to 1 decimal place)
12.
A surveyor measures an angle of elevation of to the top of a building. The surveyor is standing meters from the base. Using sin and the Pythagorean theorem, find the height of the building. (Use sin(28°) ≈ 0.469, cos(28°) ≈ 0.883)
13.
In a right triangle, the opposite side is cm and the hypotenuse is cm. Find the angle θ. (Round to the nearest degree)
14.
What is the value of ? (Give your answer as a decimal rounded to 3 decimal places)
15.
If , which of the following could be the value of θ?
1. a)Approximately 60°
2. b)Approximately 53°
3. c)Approximately 37°
4. d)Approximately 45°