Special Right Triangles and Geometry Applications Quiz

Test your knowledge with 17 questions covering Pythagorean theorem, angle ratios, and triangle properties in this trigonometry quiz.

#1

In a right-angled triangle, what is the relationship between the lengths of the legs (a and b) and the hypotenuse (c) according to the Pythagorean theorem?

a + b = c
a^2 + b^2 = c^2
a - b = c
a * b = c
#2

What are the angles of a 30-60-90 triangle?

30°, 60°, 90°
45°, 45°, 90°
60°, 60°, 60°
90°, 90°, 90°
#3

In a right-angled triangle, if one acute angle is 40 degrees, what is the measure of the other acute angle?

40 degrees
50 degrees
60 degrees
90 degrees
#4

What is the name of the theorem that states the ratio of the lengths of the sides in a 45-45-90 triangle?

Pythagorean theorem
Trigonometric theorem
Isosceles triangle theorem
Angle bisector theorem
#5

If the angles of a triangle are in the ratio 1:2:3, what type of triangle is it?

Equilateral
Isosceles
Scalene
Right-angled
#6

In a 30-60-90 triangle, what is the ratio of the length of the longer leg to the length of the shorter leg?

1:2
1:√3
√3:2
2:1
#7

In a 45-45-90 triangle, what is the ratio of the lengths of the legs to the hypotenuse?

1:1:√2
1:√2:1
√2:1:1
2:1:√3
#8

If the shorter leg of a 30-60-90 triangle is 4 units long, what is the length of the hypotenuse?

2
4
6
8
#9

If the hypotenuse of a right-angled triangle is 17 units long and one leg is 8 units long, what is the length of the other leg?

7 units
9 units
15 units
√255 units
#10

What is the relationship between the angles in a 45-45-90 triangle?

Equal
Complementary
Supplementary
Congruent
#11

If the legs of a right-angled triangle are 5 units and 12 units, what is the length of the hypotenuse?

11 units
13 units
15 units
17 units
#12

In a 45-45-90 triangle, if one leg is 10 units, what is the length of the other leg?

5 units
10 units
10√2 units
20 units
#13

A ladder is leaning against a wall, forming a right-angled triangle. If the ladder is 10 meters long and the base (distance from the wall) is 8 meters, what is the height it reaches on the wall?

6 meters
7 meters
8 meters
9 meters
#14

If the hypotenuse of a 30-60-90 triangle is 12 units long, what is the length of the shorter leg?

4 units
6 units
8 units
√48 units
#15

A right-angled triangle has angles θ, 90°-θ, and 90°. If tan(θ) = 3/4, what is the value of cos(θ)?

3/5
4/5
3/4
4/3
#16

A triangle has angles θ, 90°-θ, and 90°. If sin(θ) = 4/5, what is the value of cos(θ)?

1/5
3/5
4/5
5/4
#17

A right-angled triangle has angles θ, 90°-θ, and 90°. If cos(θ) = 5/13, what is the value of tan(θ)?

5/12
5/13
12/5
13/5

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