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Special Right Triangles
Altitudes in Right Triangles
Find the Side
Find the Angle
Solving Right Triangles
100
The angle measurement that is missing when the given angle measurements are 45 and 90 degrees.
What is 45 degrees?
100

The number of similar triangles created when an altitude is drawn to the hypotenuse of a right triangle.

What is 3?

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

The solution for solving a triangle given leg lengths 12 and 5. (Round all side lengths and angle measurements to the nearest tenth)

What are side lengths 5, 12, and 13; and angle measurements 22.6, 67.4, and 90?

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

The altitude to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of these two segments.

What is the Altitude Theorem (Rule)?  (Geometric Mean)

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
The solution for a triangle given the angle measurement 53 degrees and opposite length 2. (Round all answers to the nearest tenth.)
What are the angle measurements 37, 53, and 90 degrees; and side lengths 1.5, 2, 2.5?What is
300

The formula to find the hypotenuse in a 45-45-90 degree triangle.

What is L times the square root of 2?

300

In a right triangle, the altitude divides the hypotenuse into segments of 4 and 9. Find the length of the altitude.

What is 6? or sqrt(4*9)?

300

The missing leg length, given an angle of 52 degrees and the adjacent leg 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 solution for solving a triangle given the angle measurement 39 degrees and opposite side length 3. (Round all answers to the nearest tenth.)
What are the angle measurements 39, 51, and 90 degrees; and side lengths 3, 3.7, 4.8.
400

The formula for finding the hypotenuse in a 30-60-90 degree triangle.

What is 2s (two times s)?

400

This theorem states that each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

What is the Leg Theorem (Rule)? (Geometric Mean)

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
The solution of a triangle given an angle measurement of 49 degrees and an opposite side length of 8. (Round all angle measurements to the nearest whole degree, and all side lengths to the nearest tenth)
What is angle measurements of 41, 49, and 90; and side lengths of 7, 8, and 10.6?
500

The formula for finding the length of the longer leg in a 30-60-90 degree triangle.

What is s times the square root of 3?

500

If the altitude to the hypotenuse is 8 and one segment of the hypotenuse is 4, find the length of the other segment of the hypotenuse.

What is 16? (82 = 4x)

500
The missing adjacent side length given an angle of 41 degrees and a 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

The solution of a triangle given a leg length of 45 and a hypotenuse length of 75. (Round all angle measurements to the nearest whole degree, and all side lengths to the nearest tenth)

What are angle measurements 37, 53, and 90 degrees; and side lengths 45, 60, and 75.