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Special Right Triangles

Total questions: 52

Worksheet time: 3hrs 49mins

Name
Class
Date
1.
A square has side length 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.
a)
134.4
b)
67.2
c)
95√2
d)
(95√2)/2
2.
Find the value of y.
a)
8
b)
4
c)
2√3
d)
8√3
3.
Find the value of y.
a)
7
b)
7√3
c)
14√3
d)
(14√3)/3
4.
Find the value of y.
a)
11√2
b)
11
c)
22
d)
(11√2)/2
5.
Find the value of x.
a)
18
b)
18√3
c)
36√3
d)
12
6.
Find the value of y.
a)
9
b)
18√2
c)
9√2
d)
(9√2)/2
7.
A square tablecloth has a line of embroidered flowers along the diagonal. The tablecloth is 48 in. on each side. How long is the embroidery line?  Round to the nearest inch.
a)
48√2
b)
68
c)
34
d)
24√2
8.
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
9.
What is the length of y in this picture?
a)
45
b)
5√2
c)
90
d)
5
10.
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.
11.
What is the length of x in this 45-45-90 triangle?
a)
4√2
b)
4
c)
8
d)
4√3
12.
I have been given a hypotenuse in this 45-45-90 triangle.  How do I find the length of a leg of the triangle?
a)
Multiply by √2
b)
Divide by √2
c)
It's the same length as the hypotenuse.
d)
Divide by 2
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.
I have been given the short leg in this 30-60-90 triangle.  How do I find the length of the hypotenuse?
a)
Multiply 4 by 2
b)
Multiply 4 by √3
c)
Multiply 4 by √2
d)
Divide 4 by √3
18.
Find x.
a)
90°
b)
45°
c)
30°
d)
60°
19.

Multiply  52⋅25\sqrt{2}\cdot\sqrt{2} . 

(a)  

20.

Divide  43\frac{4}{\sqrt{3}}  

a)

 433\frac{4\sqrt{3}}{3}  

b)

 432\frac{4\sqrt{3}}{2}  

c)

 434\sqrt{3}  

21.
What type of special right triangle is this?
a)
45-45-90
b)
30-60-90
c)
not a special right triangle
22.
Find the value of x.
a)
7
b)
8
c)
9
d)
10
23.
Find the value of x.
a)
36
b)
12
c)
16
d)
25
24.
Find the value of x.
a)
15
b)
16
c)
18
d)
17
25.
Does the set of numbers represent a Pythagorean Triple.
4, 5, 6
a)
Yes
b)
No
26.
Does the set of numbers represent a Pythagorean Triple.
10, 24, 26
a)
Yes
b)
No
27.
Does the set of numbers represent a Pythagorean Triple.
15, 20, 25
a)
Yes
b)
No
28.
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
29.
The lengths of a triangle are given below. Is the the triangle obtuse, acute, or right?
11, 12, 15
a)
right
b)
obtuse
c)
acute
30.
Do the segment lengths 9, 12, and 15 form a right triangle?
a)
Yes
b)
No
c)
Maybe
d)
Pythagoras
31.
If 36 and 48 are the two smaller numbers in a Pythagorean Triple, what is the third number?
a)
45
b)
50
c)
55
d)
60
32.
Find the length of the missing side. 
a)
20 in.
b)
68 in.
c)
16 in.
d)
80 in.
33.
Find the length of the missing side. 
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
34.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
35.
solve for c
a)
7
b)
9
c)
4
d)
13
36.

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)

13.9 feet

37.

In the Old West, settlers made tents out of a piece of cloth thrown over a clothesline and then secured it to the ground with stakes forming an isosceles triangle. How long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide?

a)

14.4 feet

b)

7.2 feet

c)

10 feet

d)

20 feet

38.

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

a)

180 feet

b)

90 feet

c)

13.4 feet

d)

127.3 feet

39.

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

a)

7 inches

b)

10 inches

c)

19.7 inches

d)

13.7 inches

40.

During a football play, Odell Beckham Jr. runs a straight route 40 yards up the sideline before turning around and catching a pass thrown by Eli Manning. On the opposing team, a defender who started 20 yards across the field from Beckham saw the play setup and ran a slant towards Beckham. What was the distance the defender had to run to get to the spot where Beckham caught the ball?

a)

34.6 yards

b)

44.7 yards

c)

60 yards

d)

40 yards

41.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the other corner diagonally across the field. How far do the players run?

a)

105 meters

b)

79.4 meters

c)

210 meters

d)

150 meters

42.

How far from the base of a house do you need to place a 15' ladder so that is exactly reaches the top of a 12' wall?

a)

9 feet

b)

19.2 feet

c)

81 feet

d)

369 feet

43.

Jill's front door is 42" wide and 84" tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door?

a)

Yes

b)

No

44.

Lisa drives her car 46 km south and then 13 km east. How far is she from her starting point?

a)

44.1 km

b)

59 km

c)

47.8 km

d)

33 km

45.

Town A is 90 miles from Town B, and 18 miles from Town C. Town A, B, and C are forming a right triangle at A. A road connects towns B and C directly. Find the length of this road.

a)

108 miles

b)

91.8 miles

c)

88.2 miles

d)

72 miles

46.

Find the area of the missing square off of leg A if the area of one square is 369 and the area of another is 81?

a)

21.2

b)

17

c)

450

d)

288

47.

The three sides of triangle XYZ measure 13 meters, 17 meters, and 21 meters. Is triangle XYZ an acute, right, or obtuse triangle?

a)

Not a triangle

b)

Acute

c)

Obtuse

d)

Right

48.

The three sides of triangle DEF measure 10 meters, 7 meters, and 17 meters. Is triangle DEF an acute, right, or obtuse triangle?

a)

Not a triangle

b)

Acute

c)

Obtuse

d)

Right

49.
Find the measure of DG.
a)
14
b)
28
c)
12
d)
16
50.
Find the value of x.
a)
35
b)
3
c)
33
d)
None of these
51.
Find the value of x.
a)
23
b)
28
c)
30
d)
Cannot be determined
52.
Find the measure of the x (midsegment):
a)
25
b)
9
c)
12
d)
15

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