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Geometry: 8-1 to 8-2 (Right Triangles & Trigonometry)

Total questions: 42

Worksheet time: 2hrs 41mins

Name
Class
Date
1.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
2.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
3.

Set up an equation that could be used to solve for the variable.

a)
b)
c)
d)
4.

All of the following could be used to find angle B, EXCEPT which one?

a)
b)
c)
d)
5.

The ratio in a right triangle of adjacent to hypotenuse is _____

a)

sine

b)

cosine

c)

tangent

d)

hypotenuse

6.
We can use SOH-CAH-TOA for...
a)
Any triangle ever
b)
Non-right triangles only
c)
Right Triangles only
d)
Never
7.

What is the ratio for Sine?

a)

Hypotenuse/Opposite

b)

Opposite/Hypotenuse

c)

Opposite/Adjacent

d)

Adjacent/Opposite

8.

What is the ratio for Tangent

a)

Opposite/Adjacent

b)

Adjacent/Opposite

c)

Opposite/Hypotenuse

d)

Hypotenuse/Opposite

9.

What is the correct ratio set up for finding the tangent of Angle A? Remember: Tangent = opposite/adjacent

a)

20/12

b)

12/20

c)

12/16

d)

16/12

10.

What is the opposite side to <E?

a)

EF

b)

DF

c)

DE

11.

What is the adjacent side to <D?

a)

EF

b)

DF

c)

DE

12.
Find the measure of the indicated angle (?) round to the nearest tenth.
a)
9.4
b)
55.2
c)
20.15
d)
19.4
13.
Solve for the misssing distance
a)
18.9
b)
19.5
c)
47
d)
27.5
14.

What is the value of "x" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

15.

What is the value of "y" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

16.

Which trigonometric function would you use to find "h", the height of the tree?

a)

sine

b)

cosine

c)

tangent

d)

none of these

17.

Which expression is correct for "y"?

a)

y = tan–1(31/23)

b)

y = sin–1(31/23)

c)

y = cos–1(31/23)

18.

How would you find "x" in this Special Right Triangle?

a)

Divide 10 by 2.

b)

Multiply 10 by 2.

c)

Multiply 10 by √3

d)

Divide 10 by √3

19.
Use the Law of Sines to solve for BC
a)
33
b)
24
c)
12
d)
29
20.
Does the set of numbers represent a Pythagorean Triple.
4, 5, 6
a)
Yes
b)
No
21.
Does the set of numbers represent a Pythagorean Triple.
10, 24, 26
a)
Yes
b)
No
22.
The lengths of a triangle are given below. Is the the triangle obtuse, acute, or right?
4, 5, 6
a)
right
b)
obtuse
c)
acute
23.
Do the segment lengths 9, 12, and 15 form a right triangle?
a)
Yes
b)
No
c)
Maybe
d)
Pythagoras
24.
What is the hypotenuse if two sides are 6 and 8?
a)
10
b)
12
c)
13
d)
not enough information
25.
Find the length of the missing side. 
a)
20 in.
b)
68 in.
c)
16 in.
d)
80 in.
26.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
27.
solve for c
a)
7
b)
9
c)
4
d)
13
28.
Clint is building a wooden swing set for his children.  Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle.  To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings.  How far apart should the footings for each A-frame be?
a)
5.461 feet
b)
9.743 feet
c)
6 feet
d)
7.65 feet
29.

Do the following sides make a triangle. If so what type of triangle do they make?


Sides: 5. 13, 12

a)

Right Triangle

b)

Acute Triangle

c)

Obtuse Triangle

d)

Not a Triangle

30.
Solve for x.
a)
24.20
b)
4.92
c)
290.4
d)
29.75
31.

Elizabeth is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63.6 ft

b)

1.59 ft

c)

74.2 ft

d)

86.9 ft

32.

Kevin leans a 16 foot ladder l against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

a)

39.6

b)

6.0

c)

14.8

d)

13.6

33.
Find a.
a)
2√6
b)
2√3
c)
3
d)
6
34.
Find b.
a)
2√6
b)
2√3
c)
3
d)
6
35.
Find x.
a)
5
b)
5√2
c)
10
d)
5√3
36.
Find f.
a)
13√2
b)
13
c)
3√2
d)
26√2
37.
What type of special triangle is this?
a)
45°-45°-90°
b)
30°-60°-90°
c)
Equiangular
d)
Equilateral
38.
What type of special triangle is this?
a)
45°-45°-90°
b)
30°-60°-90°
c)
Isosceles
d)
Obtuse
39.
Find x.
a)
30°
b)
60°
c)
90°
d)
180°
40.
Find x.
a)
30°
b)
45°
c)
60°
d)
90°
41.
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 = 6 y = 3√2
42.
Find the value of x.
a)
18
b)
18√3
c)
36√3
d)
12

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