Free Printable Special Right Triangles Trig

1.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

2.

Find the value of y.

a)

9

b)

18√2

c)

9√2

d)

(9√2)/2

3.

Find the measure of the indicated angle to the nearest tenth.

a)

23.2°

b)

25.4°

c)

64.6°

d)

1°

4.

Find the measure of the indicted angle to the nearest tenth.

a)

75.1°

b)

14.9°

c)

14.4°

d)

0.3°

5.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg (y)?

a)

Multiply 4 by 2

b)

Multiply 4 by √3

c)

Multiply 4 by √2

d)

Divide 4 by 2

6.

a)

A

b)

B

c)

C

d)

D

7.

Find the value of y.

a)

7

b)

7√3

c)

14√3

d)

(14√3)/3

8.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

9.

Find x - the length of the hypotenuse of the triangle.

a)

5

b)

5√2

c)

10

d)

5√3

10.

What is the value of x?

a)

12√2

b)

2√12

c)

24

d)

12√3

11.

Right triangle ABC is shown.

Select all expressions which are equal to the length of side BC .

a)

$\sqrt[]{6^2-4.9^2}$

b)

$\frac{4.9}{\tan\left(55\right)}$

c)

$\frac{4.9}{\sin\left(55\right)}$

d)

$6\times\cos\left(55\right)$

e)

$\frac{6}{\cos\left(55\right)}$

12.

Using the ratios of a special right triangle, find the EXACT tangent of 30.

a)

√3 / 3

b)

1/2

c)

√3

d)

2

13.

Based on the side length ratio in a 30°-60°-90° or 45°-45°-90° triangle and the symmetry of the unit circle, use the drop-down arrows to choose the response that makes each statement true.

The (a) of (b) and (c) are each equal to $\sqrt[]{3}$ .

First blank is (sine/cosine/tangent). Then place the smaller of the two correct angles first.

Choose from the below words

sines

cosines

tangents

$60\degree$

$240\degree$

$30\degree$

$120\degree$

$150\degree$

$210\degree$

14.

Solve for x and y in the special right triangle.

a)

y = 4, x = 4√3

b)

y = 4√2, x = 4√2

c)

y = 4 x = 12

d)

y = 8/√3, x = 16/√3

15.

Find the value of x.

a)

18

b)

18√3

c)

36√3

d)

12

16.

Find the value of y.

a)

11√2

b)

11

c)

22

d)

(11√2)/2

17.

Right triangle ABC is shown.

Select all expressions which are equal to the length of side BC .

a)

$\sqrt[]{6^2-4.9^2}$

b)

$\frac{4.9}{\tan\left(55\right)}$

c)

$\frac{4.9}{\sin\left(55\right)}$

d)

$6\times\cos\left(55\right)$

e)

$\frac{6}{\cos\left(55\right)}$

18.

Find the missing side lengths.

a)

a = 4, b = 4

b)

a = 4, b = 2√2

c)

a = 2√2, b = 4

d)

a = 4, b = 4

19.

What is the length of RT?

a)

5

b)

5√2

c)

5√3

d)

10

20.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

Special Right Triangles Trig

Total questions: 20

Worksheet time: 20mins

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