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Triangle Trigonometry, Rotation, and Pythagorean Quiz

Total questions: 21

Worksheet time: 5hrs 15mins

Name
Class
Date
1.

Which of the following describes a 90-degree left rotation of a triangle around the origin in the coordinate plane?

a)

The triangle is flipped over the x-axis.

b)

The triangle is flipped over the y-axis.

c)

The triangle is rotated counterclockwise by 90 degrees.

d)

The triangle is rotated clockwise by 90 degrees.

2.

Given a right triangle with one angle measuring 30 degrees, what is the measure of the other non-right angle?

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

3.

In a right triangle, if the lengths of the two legs are 3 and 4, what is the length of the hypotenuse?

a)

5

b)

6

c)

7

d)

8

4.

Which trigonometric ratio is used to find the length of the opposite side of a right triangle when the angle and hypotenuse are known?

a)

Sine

b)

Cosine

c)

Tangent

d)

Cotangent

5.

If sin(θ)=12\sin(\theta) = \frac{1}{2} , what is the measure of angle θ\theta in degrees?

https://www.desmos.com/scientific

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

6.

A right triangle has a hypotenuse of length 10 and one leg of length 6. What is the length of the other leg?

https://www.desmos.com/scientific

a)

4

b)

6

c)

8

d)

9

7.

Which trigonometric function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle?

a)

Sine

b)

Cosine

c)

Tangent

d)

Secant

8.

In a right triangle, if tan(θ)=34\tan(\theta) = \frac{3}{4} , what is the ratio of the opposite side to the adjacent side?

a)

34\frac{3}{4}

b)

43\frac{4}{3}

c)

13\frac{1}{3}

d)

14\frac{1}{4}

9.

What is the Pythagorean theorem formula?

a)

a2+b2=c2a^2 + b^2 = c^2

b)

a2b2=c2a^2 - b^2 = c^2

c)

a2+b2=ca^2 + b^2 = c

d)

a+b=c2a + b = c^2

10.

If a right triangle has one angle measuring 30 degrees with the hypotenuse measuring 6 units. What is the length of the adjacent leg? Round to the nearest whole number.

https://www.desmos.com/scientific

a)

3

b)

4

c)

5

d)

6

11.

A triangle is rotated 180 degrees around the origin. What is the effect on the coordinates of its vertices?

a)

The x-coordinates are negated.

b)

The y-coordinates are negated.

c)

Both x and y coordinates are negated.

d)

The coordinates remain unchanged.

12.

In a right triangle, if one angle is 45 degrees, what is the measure of the other non-right angle?

https://www.desmos.com/scientific

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

13.

Which trigonometric function is defined as the ratio of the opposite side to the adjacent side in a right triangle?

a)

Sine

b)

Cosine

c)

Tangent

d)

Cosecant

14.

If tan(θ)=1\tan(\theta) = 1 , what is the measure of angle θ\theta in degrees?

https://www.desmos.com/scientific

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

15.

A right triangle has legs of lengths 5 and 12. What is the length of the hypotenuse?

https://www.desmos.com/scientific

a)

10

b)

13

c)

15

d)

17

16.

Which trigonometric ratio is used to find the length of the adjacent side of a right triangle when the angle and hypotenuse are known?

a)

Sine

b)

Cosine

c)

Tangent

d)

Secant

17.

If sin(θ)=32\sin(\theta) = \frac{\sqrt{3}}{2} , what is the measure of angle θ\theta in degrees?

https://www.desmos.com/scientific

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

18.

A triangle is rotated 270 degrees counterclockwise around the origin. What is the effect on the coordinates of its vertices?

a)

The x-coordinates become the y-coordinates, and the y-coordinates become the negative x-coordinates.

b)

The x-coordinates become the negative y-coordinates, and the y-coordinates become the x-coordinates.

c)

Both x and y coordinates are negated.

d)

The coordinates remain unchanged.

19.

In a right triangle, if cos(θ)=12\cos(\theta) = \frac{1}{2} , what is the measure of angle θ\theta in degrees?

https://www.desmos.com/scientific

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

20.

Which would you choose to find the degree of an angle?

a)

Sine to the negative 1

b)

Cosine

c)

Tangent

d)

Secant

21.

Bonus: worth an extra point!

if a triangle has hypotenuse = 14, adjacent angle = 60 degrees, what is the measure of the adjacent side?

The adjacent side would measure 7.

a)
True
b)
False