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Topic 8 - Rights Triangles and Trigonometry Review

Total questions: 47

Worksheet time: 1hrs 27mins

Name
Class
Date
1.

Which side of the triangle is the hypotenuse?

a)

QP

b)

QR

c)

RP

2.

Which is the formula used for the Pythagorean Theorem?

a)

a2+b2+c2

b)

a+b=c

c)

a2+c2=b2

d)

a2+b2=c2

3.

Find the value of x. Round to the nearest tenth if needed.

a)

10.6

b)

36.9

c)

18.2

d)

20

4.

Classify the triangle (if possible) as Acute, Right, or Obtuse given the three side measures: 12, 13, 17

a)

Acute

b)

Right

c)

Obtuse

d)

Not Possible

5.
Solve for x and y in the special right triangle.
a)
x = 7, y = 7√2
b)
x = 14 y = 7√2
c)
x = 14√2 y = 7√2
d)
x = 14 y = 14√2
6.
Solve for a and b in the special right triangle.
a)
a = 5, b = 5
b)
a = 10, b = 10√2
c)
a = 10√2, b = 10√2
d)
a = 5√2, b = 5√2
7.
Solve for u and v in the special right triangle.
a)
v = 9√3, u = 6√3
b)
v = 6√3 u = 9√3
c)
v = 9, u = 6√3
d)
v = 3√6, u = 6√3
8.
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
9.
Choose the correct ratio.
a)
sin(37)=x/14
b)
cos(37)=x/14
c)
tan(37)=x/14
d)
sin(37)=14/x
10.

a=3, b=4, and c=5

Is this a right triangle?

a)

yes

b)

no

11.

a=3, b=6, and c=9

Is this a right triangle?

a)

yes

b)

no

12.

Which side lengths would form a right triangle?

a)

3, 5, 6

b)

2, 8, 10

c)

3, 4, 5

d)

7, 12, 15

13.
A 10-foot ladder is leaning against the wall.  The bottom of the ladder is 4 feet from the base of the wall.  Which of the following is closest to the distance from the top of the ladder to the base of the wall?
a)
9ft
b)
11ft
c)
6ft
d)
14ft
14.
The bottom of a 13-foot straight ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach? 
a)
12 feet
b)
13.5 feet
c)
13 feet
d)
11.6 feet
15.
What is the longest side of a right triangle called?
a)
Leg A
b)
Leg B
c)
Hypotenuse
d)
Pythagoras' Big Buddy
16.

what is the length of the diagonal of the rectangle?

a)
50
b)
60
c)
70
d)
80
17.
Find x.
a)
10
b)
10√3
c)
10√2
d)
20
18.

Find x.

a)

22

b)

11311\sqrt{3}

c)

11211\sqrt{2}

d)

11

19.

Find x.

a)

9

b)

333\sqrt{3}

c)

6

d)

636\sqrt{3}

20.

The area of a square is 36 square cm. What is the length of the diagonal? (round to the nearest tenth.)

(a)  

21.

The area of a square is 81 square cm. What is the length of the diagonal? (round to the nearest tenth.)

(a)  

22.

What do the angles in an equilateral triangle measure?

a)

30°, 60°, 90°

b)

60°, 60°, 60°

c)

45°, 45°, 90°

d)

35°, 55°, 90°

23.
From ∠C, what side is AB?
a)
Adjacent
b)
Hypotenuse
c)
Opposite
24.

Which letter represents the HYPOTENUSE?

a)

A

b)

B

c)

C

25.

Which letter represents the ADJACENT side to angle a?

a)

A

b)

B

c)

C

26.

Which of the following is the correct ratio for tan C?

a)

27/36

b)

27/45

c)

36/45

d)

36/27

27.
a)
A
b)
B
c)
C
d)
D
28.
Which ratio would you use to solve for x?
a)
sine
b)
cosine
c)
hypotenuse
d)
tangent
29.
Which equation would you use to solve for x?
a)
sin 58 = x/19
b)
cos 58 = x/19
c)
sin 58 = 19/x
d)
cos 58 = 19/x
30.
Solve for the missing distance.
a)
18.9
b)
19.5
c)
47
d)
27.5
31.
A ladder is leaning against a house at an angle of 39 degrees. If the ladder is 12 ft. long, how far is the bottom of the ladder from the house? 
a)
15.4 ft.
b)
9.3 ft.
c)
20.2 ft. 
d)
5.3 ft. 
32.

A 30 ft. wire stretches from the top of a light pole diagonally to the ground. The light pole is 10 feet high. What is the angle the wire makes with the ground? Round to the nearest whole degree.

a)

66 degrees

b)

80 degrees

c)

30 degrees

d)

19 degrees

33.

A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun.

a)

34 degrees

b)

56 degrees

c)

72 degrees

d)

15 degrees

34.

Solve for the missing angle.

a)

50.5 degrees

b)

12.7 degrees

c)

36.9 degrees

d)

72.2 degrees

35.

In the given figure, what is the angle of elevation?

a)

∠B

b)

∠D

c)

∠C

d)

∠A

36.
Find the measure of the angle.  Round to the nearest tenth. 
a)
30.8
b)
32.1
c)
34.3
d)
36.9
37.
Find the length of side w.
a)
21.4 cm
b)
18.0 cm
c)
36.5 cm
d)
43.6 cm
38.
Choose the correct ratio.
a)
sin-1(9/20)
b)
cos-1(9/20)
c)
tan-1(9/20)
d)
cos-1(20/9)
39.
Solve for the missing angle
a)
50.2
b)
93.1
c)
12.6
d)
42.2
40.
Solve for x. Round to the nearest tenth.
a)
9.8
b)
0.1
c)
0.038
d)
9.9
41.

Calculate the area of the triangle, correct to one d.p.

(a)  

42.

Calculate the area of the triangle, correct to one d.p.

(a)  

43.

What is the formula for finding the area of a triangle using sine?

a)

a * b * sin(C)

b)

(1/2) * a * b * cos(C)

c)

(1/2) * a * b * tan(C)

d)

(1/2) * a * b * sin(C)

44.

Find the exact area of the triangle

a)

13.9 in2

b)

13.8 in2

c)

14.0 in2

d)

27.9 in2

45.

If sin x = cos y, what must be true about x and y?

a)

x + y = 90⁰

b)

x = y 

c)

x = 2y

46.

cos 40⁰ = ?

a)

sin 50⁰

b)

cos 50⁰

c)

tan 50⁰

47.

sin 20⁰ = ?

a)

cos 70⁰

b)

sin 70⁰

c)

cos 20⁰

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