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WorksheetsLegs and Hypotenuse of Right Triangles
Total questions: 24
Worksheet time: 34mins
Name
Class
Date
1.
If an triangle is a 45-45-90 triangle. And the hypotenuse is 4√2. What are the length of the legs?
a)
4
b)
4√3
c)
8
d)
8√2
2.
What type of triangle will have x√2 and x√2 and x
a)
45-45-90
b)
60-70-50
c)
30-60-90
d)
40-50-70
3.
Find out what is the length of leg KL?
a)
3
b)
2
c)
5
d)
4
4.
Which ratio corresponds to cos 35?
a)
3.0/7.8
b)
4.2/7.8
c)
4.2/3.0
d)
3.0/4.2
5.
Which ratio represents cos A in the accompanying diagram ΔABC?
a)
13/5
b)
12/5
c)
12/13
d)
5/13
6.
What is the value of tan(θ)?
a)
7/25
b)
7/24
c)
25/24
d)
24/25
7.
Find tangent using the angle Φ.
a)
4/3
b)
4/5
c)
3/4
d)
5/3
8.
Two trees stand opposite one another, at points A and B, on opposite banks of a river. Distance AC along one bank is perpendicular to BA, and is measured to be 100 feet. Angle ACB is measured to be 79°. How far apart are the trees; that is, what is the width w of the river?
a)
514.5 ft
b)
527.3 ft
c)
514.5 m
d)
527.3 m
9.
What is the measure of angle A in the right triangle below?
a)
43°
b)
38°
c)
27°
d)
52°
10.
Find sin(x) and cos(x) in the right triangle shown below.
a)
sin(x) = 6/10 = 0.6
cos(x) = 8/10 = 0.8
cos(x) = 8/10 = 0.8
b)
sin(x) = 8 / 10 = 0.8
cos(x) = 6 / 10 = 0.6
cos(x) = 6 / 10 = 0.6
c)
sin(x) = 3/10 = 0.3
cos(x) = 5/10 =0.5
cos(x) = 5/10 =0.5
d)
sin(x) = 5/10 = 0.5
cos(x) = 3/10 = 0.3
cos(x) = 3/10 = 0.3
11.
Which one of the following is a Pythagorean triple?
a)
21, 27, 35
b)
12, 35, 37
c)
33, 35, 48
d)
34-45-56
12.
Which one of the following is NOT a Pythagorean triple?
a)
7, 24, 25
b)
8, 15, 17
c)
9, 12, 15
d)
10, 16, 19
13.
If (16, 30, y) is a Pythagorean triple, what is the value of y?
a)
48
b)
45
c)
34
d)
32
14.
One angle of a right-angled triangle is 67°
What is the size of another angle of the triangle?
What is the size of another angle of the triangle?
a)
13
b)
27
c)
23
d)
17
15.
One angle of a right-angled triangle is 39°
What is the size of another angle of the triangle?
What is the size of another angle of the triangle?
a)
54
b)
141
c)
51
d)
65
16.
A ladder 6 feet long leans against a wall and makes an angle of 71º with the ground. Find to the nearest tenth of a foot how high up the wall the ladder will reach.
a)
2.0 ft
b)
3.5 ft
c)
5.7 ft
d)
6.0 ft
17.
What are the measurements of a and b?
a)
a=2
b=2
b=2
b)
a=4
b=4
b=4
c)
a=6
b=6
b=6
d)
a=8
b=8
b=8
18.
Find x
a)
x=2
b)
x=3
c)
x=4
d)
x=1
19.
Find x
a)
x=6
b)
x=2√3
c)
x=3√3
d)
x=4
20.
A six-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? How far from the wall is the base of the ladder? Round your answers to two decimal places, as needed.
a)
4
b)
3
c)
5
d)
2
21.
A 16 foot ladder is leaning against a house. It touches the bottom of a window that is 12 feet 6 inches above the ground. What is the measure of the angle that the ladder forms with the ground?
a)
48.6°
b)
26.6°
c)
57.9°
d)
43.9°
22.
If Brooke is installing a wide-screen television with a 60-inch diagonal. Her entertainment center is 48 inches wide by 36 inches high, will the television fit in her current entertainment center?
a)
57
b)
38
c)
60
d)
48
23.
Given an acute angle and one side. Solve the right triangle ABC if angle A is 36°, and side c is 10 cm.
a)
4.75
b)
6.39
c)
5.88
d)
37
24.
Find side AB
a)
15.8
b)
34.2
c)
52.4
d)
12.0
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