Special Right Triangles Quiz
Questions: 16 · 10 minutes
1. A square has a diagonal of 12. What is the exact length of one side?
4√3
6
12√2
6√2
2. In a 30-60-90 triangle, the hypotenuse is 18. What is the length of the leg opposite the 60° angle?
6√3
9
18√3
9√3
3. A right triangle has side lengths 5, 5, and 5√2. Which description is correct?
It is a 45-45-90 triangle.
It is a 30-60-90 triangle.
It is right but not a special right triangle.
The listed lengths cannot form a right triangle.
4. In a 30-60-90 triangle, what is the ratio of the shortest leg to the longer leg to the hypotenuse?
1 : √3 : 2
1 : √2 : 2
√2 : √3 : 2
1 : 2 : √3
5. The longer leg of a 30-60-90 triangle is 9. What is the exact length of its shortest leg?
3
9√3
3√3
9/2
6. A 14-foot ladder forms a 30° angle with level ground. Assuming the ladder is the hypotenuse, how high up the wall does it reach?
About 12.1 feet
14 feet
About 24.2 feet
7 feet
7. A 45-45-90 triangle has a hypotenuse of 10. What is the length of each leg?
5
5√2
10√2
10/√3
8. On a coordinate grid, a line segment moves 6 units right and 6 units up. What is the exact length of the segment?
6√2
12
6√3
3√2
9. An equilateral triangle has side length 12. An altitude divides it into two 30-60-90 triangles. What is the altitude's length?
6√2
12√3
6√3
8√3
10. In a right triangle, one leg is exactly half as long as the hypotenuse. What is the measure of the angle opposite that leg?
45°
60°
30°
75°
11. The shortest leg of a 30-60-90 triangle is 7. What is the length of the longer leg?
7√2
7√3
14√3
14
12. A diagonal divides a square with side length 8 into two congruent right triangles. What is the area of either triangle?
16 square units
32 square units
32√2 square units
64 square units
13. An isosceles right triangle has a hypotenuse of 8. What is the length of either leg?
8√2
4
8/√3
4√2
14. A 30-60-90 triangle has a shortest leg of 4. What is its exact perimeter?
8 + 4√3
12 + 8√3
12 + 4√3
8 + 8√3
15. Which side-length ratio describes a 45-45-90 triangle, with the hypotenuse listed last?
1 : 1 : √2
1 : √2 : 2
1 : √3 : 2
1 : 2 : √3
16. A 30-60-90 triangular tile has a hypotenuse of 10 units. What is its exact area?
25√3 square units
25√3/2 square units
50√3 square units
25/2 square units