Special Right Triangles
Trig Ratios
Find the Side
Find the Angle
Application Problems
100
The angle measurement that is missing when the given angle measurements are 45 and 90 degrees.
What is 45 degrees?
100
The trig ratio used when given the adjacent and hypotenuse lengths.
What is cosine?
100
The missing hypotenuse length given side lengths 9 and 12. (Round to the nearest tenth.)
What is 15?
100
The missing angle in a triangle given angle measurements 29 and 90 degrees.
What is 61?
100

From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

x = 59.3 m

200
The missing angle measurement when the given angle measurements are 60 and 90 degrees.
What is 30 degrees?
200

The road sign is shaped like an equilateral triangle. If the length of each side is  36 inches, estimate the area of the sign by finding the area of the equilateral triangle. Write as a decimal, round to nearest tenth. 

What is 561.2 inches squared?

200
The missing hypotenuse length given the angle 72 degrees and adjacent side length of 6. (Round to the nearest tenth)
What is 19.4?
200
The missing angle in a triangle given adjacent side length 16 and hypotenuse 20.3 (Round to the nearest whole degree)
What is 38 degrees?
200

In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearest tenth of a cm, how long is that leg?

What is 36.5 cm?

300
The formula to find the hypotenuse in a 45-45-90 degree triangle. [Hint: Use the textbook formulas.]
What is x times the square root of 2?
300
The sine of a triangle with angle A and opposite side length 4 and hypotenuse length 20. (Round to the nearest tenth)
What is 0.2?
300
The missing side length given an angle of 52 degrees and the adjacent side length of 12.5. (Round to the nearest whole number)
What is 16?
300
The missing angle measurement given an opposite side length of 5 and a hypotenuse length of 10.3 (Round to the nearest whole degree)
What is 29 degrees?
300

The diagonal of a square is 16 cm. What is the area?

128 cm squared

400

The diagonal of a square is 16. What is the length of the side in simplest radical form?

What is 8 radical 2?

400
The tangent of a triangle with angle Z and adjacent side length 15 and opposite side length 10. (Round to the tenths place)
What is 0.7?
400
The missing opposite side length given an angle of 53 degrees and a hypotenuse of length 2.5 (Round to the nearest whole number.)
What is 2?
400
The two angle measurements given the same side lengths of 3.
What is 45 and 45 degress?
400

A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52 degrees. How high off the ground is the kite? How far away is the man from the spot directly under the kite? (round to nearest tenth)

Height of kite is 78.8 ft and man is 61.6 ft away from base of kite

500
The formula for finding the length of the longer leg in a 30-60-90 degree triangle.
What is x times the square root of 3?
500
The cosine of a triangle with angle A and opposite side length 5 and hypotenuse length 13.
What is 0.9?
500

The missing adjacent side length given an angle of 41 degrees and an opposite side length of 7. (Round to the nearest whole number.)

What is 8?

500
The missing angle measurement given opposite side length 6.3 and adjacent side length 9. (Round to the nearest whole degree)
What is 35?
500

From an airplane at an altitude of 1200 m, the angle of depression to a building on the ground measures 28°. Find the distance from the plane to the building.

What is 2,256.87 ft?

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