Right Triangles
Name:
1.
Date:
A ship at sea heads directly toward a cli on the
shoreline. The accompanying diagram shows the
top of the cli , D, sighted from two locations, A
and B, separated by distance S. If mODAC = 30,
mODBC = 45, and S = 30 feet, what is the height
of the cli , to the nearest foot?
5.
In the diagram below of right triangle ABC, CD
is the altitude to hypotenuse AB, CB = 6, and
AD = 5.
What is the length of BD ?
A.
2.
B.
9
C.
3
D. 4
The “Little People” day care center has a
rectangular, fenced play area behind their building.
The play area is 30 meters long and 20 meters
wide. Find, to the nearest meter, the length of a
pathway that runs along the diagonal of the play
area.
6.
3.
5
In the diagram below of right triangle ACB,
altitude CD is drawn to hypotenuse AB .
A cable 20 feet long connects the top of a agpole
to a point on the ground that is 16 feet from the
base of the pole. How tall is the agpole?
A.
8 ft
B.
10 ft
C.
12 ft
D. 26 ft
If AB = 36 and AC = 12, what is the length of
AD ?
4.
A.
If the length of a rectangular television screen is
20 inches and its height is 15 inches, what is the
length of its diagonal, in inches?
A.
5
B.
13.2
C.
25
D. 35
page 1
32
B.
6
C.
3
D. 4
7.
In the diagram below, the length of the legs
AC and BC of right triangle ABC are 6 cm and
8 cm, respectively. Altitude CD is drawn to the
hypotenuse of ^ABC.
9.
What is the exact height of the pole, in meters?
What is the length of AD to the nearest tenth of a
centimeter?
A.
8.
3.6
B.
6.0
C.
6.4
The accompanying diagram shows two cables of
equal length supporting a pole. Both cables are
14 meters long, and they are anchored to points in
the ground that are 14 meters apart.
A.
7
B.
p
7 2
C.
p
7 3
D. 14
D. 4.0
10.
In the accompanying diagram of right triangles
ABD and DBC, AB = 5, AD = 4, and CD = 1.
Find the length of BC to the nearest tenth.
11.
The altitude drawn to the hypotenuse of a right
triangle divides the hypotenuse into segments of
lengths 4 and 12. The length of the shorter leg of
the right triangle is
The accompanying diagram shows ramp RA
leading to level platform AM, forming an angle of
45 with level ground. If platform AM measures
2 feet and is 6 feet above the ground,
explain why
p
the exact length of ramp RA is 6 2 feet.
A.
12.
B.
p
20
C.
p
48
D.
p
192
Right triangle ABC has a right angle at C, altitude
CD is drawn, AC = 10, and AB = 20. What is the
length of AD?
A.
page 2
8
p
200
B.
2
C.
40
D. 5
Right Triangles
13.
In the accompanying diagram of rectangle ABCD,
DE is perpendicular to diagonal AC. If AE = 3
and EC = 9, what is the length of AD ?
A.
p
C.
5
27
B.
16.
6
D. 4
17.
14.
In ^ABC, mOC = 90. If AB = 5 and AC = 4,
which statement is not true?
A.
cos A =
4
5
B.
tan A =
3
4
C.
sin B =
4
5
D. tan B =
5
3
In right triangle ABC shown below, AB = 18:3 and
BC = 11:2.
In the diagram below of right triangle JTM,
JT = 12, JM = 6, and mOJMT = 90.
What is the measure of OA, to the nearest tenth
of a degree?
A.
What is the value of cot J ?
A.
15.
p
3
3
B.
2
C.
p
3
D.
p
2 3
3
18.
31.5
B.
37.7
C.
52.3
D. 58.5
As shown in the diagram below, a ladder 5 feet
long leans against a wall and makes an angle of
65 with the ground. Find, to the nearest tenth of
a foot, the distance from the wall to the base of
the ladder.
In the diagram
below of
p
p ^ADB, mOBDA = 90,
AD = 5 2, and AB = 2 15.
What is the length of BD ?
A.
p
10
B.
p
20
C.
p
50
D.
p
110
page 3
Right Triangles
19.
An 8-foot rope is tied from the top of a pole to
a stake in the ground, as shown in the diagram
below.
21.
To the nearest tenth of a degree, what is the
measure of the largest acute angle in the triangle?
If the rope forms a 57 angle with the ground,
what is the height of the pole, to the nearest tenth
of a foot?
A.
4.4
B.
6.7
C.
9.5
A.
32.0
B.
38.7
C.
51.3
D. 90.0
D. 12.3
22.
20.
In the diagram of ^ABC shown below, BC = 10
and AB = 16.
Which equation could be used to nd the measure
of one acute angle in the right triangle shown
below?
Which equation shows a correct trigonometric ratio
for angle A in the right triangle below?
A.
sin A =
15
17
B.
tan A =
8
17
C.
cos A =
15
17
D. tan A =
15
8
23.
A.
sin A =
4
5
B.
tan A =
5
4
C.
cos B =
5
4
D. tan B =
5
4
In right triangle ABC, mOC = 90, mOA = 55, and
CA = 10. What is the length of AB to the nearest
integer?
A.
page 4
6
B.
14
C.
17
D. 24
Right Triangles
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Right Triangles
10/24/2013
1.
Answer:
41
21.
Answer:
C
2.
Answer:
36, and appropriate work is shown.
22.
Answer:
A
3.
Answer:
C
23.
Answer:
C
4.
Answer:
C
5.
Answer:
D
6.
Answer:
D
7.
Answer:
A
8.
Answer:
[task]
9.
Answer:
C
10.
Answer:
2.8
11.
Answer:
A
12.
Answer:
D
13.
Answer:
B
14.
Answer:
A
15.
Answer:
A
16.
Answer:
D
17.
Answer:
A
18.
Answer:
2.1
19.
Answer:
B
20.
Answer:
C