Introduction to Trigonometric Ratios

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Show your work for each problem.

1.
In SOH-CAH-TOA, what does 'SOH' stand for?
1. a)Sine = Opposite / Hypotenuse
2. b)Sine = Hypotenuse / Opposite
3. c)Sine = Opposite / Adjacent
4. d)Sine = Adjacent / Hypotenuse
2.
Which side of a right triangle is always the longest?
1. a)Adjacent
2. b)Opposite
3. c)It depends on the angle
4. d)Hypotenuse
3.
In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is ? Express as a decimal.
4.
In a right triangle, if the adjacent side is 4 and the hypotenuse is 5, what is ? Express as a decimal.
5.
Which trigonometric ratio uses the opposite and adjacent sides (not the hypotenuse)?
1. a)Tangent
2. b)Secant
3. c)Cosine
4. d)Sine
6.
In a right triangle, if the opposite side is 5 and the adjacent side is 12, what is ? Express as a fraction (e.g., 5/12).
7.
A right triangle has sides 5, 12, and 13. Find all three trigonometric ratios for the angle opposite the side of length 5.
8.
If , what can you conclude about the opposite side and hypotenuse?
1. a)The opposite is twice the hypotenuse
2. b)The opposite equals the hypotenuse
3. c)The adjacent is half the hypotenuse
4. d)The opposite is half the hypotenuse
9.
In a right triangle, the opposite side is 8 and the hypotenuse is 10. Find all three trigonometric ratios.
10.
If , what must be true about the opposite and adjacent sides?
11.
A ladder 10 meters long leans against a wall. The base is 6 meters from the wall. Find the sine of the angle the ladder makes with the ground.
12.
For which angle is ?
1. a)45 degrees
2. b)90 degrees
3. c)60 degrees
4. d)30 degrees
13.
In a right triangle, . Find and .
14.
If and the hypotenuse is 15, what is the length of the adjacent side?
15.
A ramp rises 3 meters over a horizontal distance of 4 meters. Find the sine, cosine, and tangent of the angle the ramp makes with the ground.