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Worksheets

Special Right Triangles and Trig Functions

Total questions: 50

Worksheet time: 3hrs 40mins

Name
Class
Date
1.
What type of special triangle is this?
a)
45°-45°-90°
b)
30°-60°-90°
c)
Equiangular
d)
Equilateral
2.
What type of special triangle is this?
a)
45°-45°-90°
b)
30°-60°-90°
c)
Isosceles
d)
Obtuse
3.
Find x.
a)
30°
b)
60°
c)
90°
d)
180°
4.
Find x.
a)
30°
b)
45°
c)
60°
d)
90°
5.
Find x.
a)
10
b)
√3
c)
5
d)
10√3
6.
Find x.
a)
4
b)
2
c)
√3
d)
2√2
7.
Find x.
a)
10
b)
20
c)
10√3
d)
√3
8.
Find x.
a)
12
b)
√2
c)
√3
d)
6
9.
In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...
a)
Multiply that leg by 2
b)
Use the same length for the second leg
c)
Multiply that leg by √2
d)
Divide that leg by √2
10.
What is the length of y in this picture?
a)
45
b)
5√2
c)
90
d)
5
11.
In this 45-45-90 triangle, I have been given the length of a leg.  How do I find the length of the hypotenuse?
a)
It is the same length as the given leg.
b)
Multiply that leg's length by √2.
c)
Multiply that leg's length by 2.
d)
Divide that leg's length by √2.
12.
What is the length of x in this 45-45-90 triangle?
a)
4√2
b)
4
c)
8
d)
4√3
13.
What is the length of y in this 45-45-90 triangle?
a)
8√2
b)
4√2
c)
4
d)
8
14.
Which side is the long leg in this 30-60-90 triangle?
a)
4
b)
u
c)
v
15.
Which side is the short leg of this 30-60-90 triangle?
a)
6
b)
m
c)
n
16.
I have been given the short leg in this 30-60-90 triangle.  How do I find the long leg?
a)
Multiply 4 by 2
b)
Multiply 4 by √3
c)
Multiply 4 by √2
d)
Divide 4 by 2
17.
What is the length of u and v in this 30-60-90 triangle?
a)
u = 8 v = 4√3
b)
u = 4√2 v = 8
c)
u = 16 v = 8
d)
u = 4√3 v = 8
18.
I have been given the long leg in this 30-60-90 triangle.  How do I find the short leg?
a)
Multiply 7 by 2
b)
Multiply 7 by √3
c)
Divide 7 by 2
d)
Divide 7 by √3
19.
What is the formula used to solve for the hypotenuse?
a)

c2 = a2 + b2

b)

a2 + b = c

c)

a-b=c

d)

c2 = a2 + b

20.
solve for x
a)
5552363959656.
b)
10
c)
100
d)
89
21.
Find the length of the missing side. 
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
22.
What is the value of x in the right triangle shown?
a)
16cm
b)
18cm
c)
24cm
d)
√674cm
23.
What is the length of x in this 45-45-90 triangle?
a)
4√2
b)
4
c)
8
d)
4√3
24.
I have been given the long leg in this 30-60-90 triangle.  How do I find the hypotenuse?
a)
Divide 8 by √3
b)
Divide 8 by 2
c)
Divide 8 by 2, then multiply that answer by √2
d)
Divide 8 by √3, then multiply that answer by 2
25.
What are x and y in this 30-60-90 triangle?
a)
x = 6 y = 3√3
b)
x = 3√2 y = 3
c)
x = 3√3 y = 6
d)
x = 3√3 y = 3√2
26.
Which set of sides would make a right triangle?
a)
4,5,6
b)
8,10,12
c)
5,12,13
d)
5,10,12
27.
Acute, right, or obtuse?
a)
Acute
b)
Right
c)
Obtuse
d)
I don't know
28.

Does the set of numbers represent a right triangle?

20, 25, 15

a)

Yes

b)

No

29.

Determine what type of triangle is given by the sides 4,5,6

a)

Not a triangle

b)

right

c)

obtuse

d)

acute

30.

Is a figure with the given sides 0.3, 0.4, 0.5 a triangle

a)

not a triangle

b)

triangle

31.
What is the correct ratio?
a)
sin 40 = w/28
b)
cos 40 = w/28
c)
tan 40 = w/28
d)
sin 40 = 28/w
32.

If you are given the two sides that are not the hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

33.
If you are given the opposite side and hypotenuse, which trig function should you use?
a)
sine
b)
cosine
c)
tangent
d)
cotangent
34.

If you are given two parts of an obtuse triangle, which trig function should you use to find other missing parts?

a)

sine

b)

cosine

c)

tangent

d)

You can only use SOHCAHTOA rules on right triangles.

35.
Which is the correct set up to solve for x?
a)
sin 24 = x / 12
b)
cos 24 = x / 12
c)
tan 24 = x / 12
36.
Which is the correct set up to solve for x?
a)
sin 72 = 6 / x
b)
cos 72 = 6 / x
c)
tan 72 = 6 / x
37.
Which is the correct set up to solve for x?
a)
sin 51 = 14 / x
b)
cos 51 = x / 14
c)
sin 51 = x / 14
d)
cos 51 = 14 / x
38.

If you are given the two sides that are not the hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

39.
If you are given the opposite side and hypotenuse, which trig function should you use?
a)
sine
b)
cosine
c)
tangent
d)
cotangent
40.
Which is the correct set up to solve for x?
a)
sin 24 = x / 12
b)
cos 24 = x / 12
c)
tan 24 = x / 12
41.
Which is the correct set up to solve for x?
a)
sin 72 = 6 / x
b)
cos 72 = 6 / x
c)
tan 72 = 6 / x
42.
Which is the correct set up to solve for x?
a)
sin 51 = 14 / x
b)
cos 51 = x / 14
c)
sin 51 = x / 14
d)
cos 51 = 14 / x
43.

Find the missing side.

a)

11.6

b)

93.4

c)

31.9

d)

1.1

44.
a)
20
b)
5.9
c)
33
d)
42
45.

Find the missing side.

a)

25.7

b)

10.9

c)

5.1

d)

6.2

46.

Find the missing side.

a)

13.3

b)

31.3

c)

14.4

d)

7.5

47.

Which equation is true?

a)

sin (x) = 14/29

b)

cos (x) = 14/29

c)

tan (x) = 14/29

d)

tan (x) = 29/14

48.

Which equation is true?

a)

sin (x) = 11/27

b)

sin (x) = 27/11

c)

cos (x) = 11/27

d)

tan (x) = 11/27

49.
Find the length of side w.
a)
21.4 cm
b)
18.0 cm
c)
36.5 cm
d)
43.6 cm
50.

Will you be studying for the quiz?

a)

yes

b)

no

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