Mixed Word
Pythagorean
Problems
Theorem
(Regents)
Sine
Cosine
Tangent
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
40
50
50
50
50
50
10 points
What is the ratio for the sine of
an angle?
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Answer
10 points
A N S W E R:
Sin  
Opposite
Hypotenuse
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20 points
Find the value of x to the nearest
hundredth:
20 '
x
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40 
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Answer
20 points
A N S W E R:
x  12 . 86 '
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30 points
Find the measurement of angle x
12 "
24 "
x
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Answer
30 points
A N S W E R:
x  30 
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40 points
A ladder 10 feet long is leaning
against a house making an angle of
71  with the ground. Find to the
nearest tenth of a foot how high up
the house the ladder reaches?
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Answer
40 points
A N S W E R:
9.5 feet
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50 points
An airplane is flying at an altitude of 3000 ft. The
angle of depression of the airport ground signal
Measures 27  . Find to the nearest foot the distance
Between the airplane and the airport signal.
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Answer
50 points
A N S W E R:
6,608 feet
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10 points
What is the ratio for the cosine of
an angle?
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Answer
10 points
A N S W E R:
Cos  
Adjacent
Hypotenuse
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20 points
Find the value of x to the nearest whole number
30cm
x
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38 
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Answer
20 points
A N S W E R:
X=24
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30 points
Find the value of x to the nearest
tenth of a degree
x
10’
8’
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Answer
30 points
A N S W E R:
x  36 . 9 
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40 points
A wire 3 meters in length, is attached
from the top of a post to a stake in the
ground. The wire makes a 35  angle
with the ground. To the nearest
hundredth of a meter, find the distance
from the wire on the ground to the post.
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40 points
A N S W E R:
x  2 . 46
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50 points
A child's slide is 9 meters long and is
built over a horizontal distance of 6
meters along the ground. Find to the
nearest degree the measure of the
angle that the slide makes with the
ground.
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Answer
50 points
A N S W E R:
x  48 
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10 points
What is the ratio for the tangent of an angle?
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Answer
10 points
A N S W E R:
Tan  
Opposite
Adjacent
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20 points
Find the value of x:
12
45 
x
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Answer
20 points
A N S W E R:
X=12
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30 points
Find the measure
of x to the nearest
4
degree.
x
14
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Answer
30 points
A N S W E R:
x  74 
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40 points
At a point on the ground 50 meters from the
foot of a tree, the measure of the angle of
elevation of the top of the tree is 48  . Find
the height of the tree to the nearest meter.
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Answer
40 points
A N S W E R:
56 meters
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50 points
Find to the nearest degree the
measure of the angle of elevation
of the sun when a woman 5foot
tall cast a 3 foot shadow
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Answer
50 points
A N S W E R:
59 
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10 points
What is the Pythagorean theorem
and when is it used?
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Answer
10 points
A N S W E R:
The Pythagorean theorem is a 2  b 2  c 2 and it is
used to find side lengths of a right triangle.
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20 points
Find x:
x
6
6
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Answer
20 points
A N S W E R:
6 2  8 . 49
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30 points
The lengths of the sides of a triangle are 8,
15, and 17. Is this a right triangle?
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Answer
30 points
A N S W E R:
Yes
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40 points
If the length of the diagonal of a
rectangle is 26 in and the length of its
base is 24 in, find the length of the
altitude of the rectangle.
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Answer
40 points
A N S W E R:
X=10
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50 points
The length of a rectangle is 7 feet more then
its width. A diagonal of a rectangle measures
17 meters. Find the length and width of
rectangle.
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Answer
50 points
A N S W E R:
Width = 8, Length = 15
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10 points
The accompanying diagram shows a kite
that has been secured to a stake in the
ground with a 20-foot string. The kite is
located 12 feet from the ground, directly
over point X. What is the distance, in feet,
between the stake and point X?
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10 points
A N S W E R:
16 feet
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20 points
Find, to the nearest tenth
of a foot, the height of the
tree represented in the
accompanying diagram.
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Answer
20 points
A N S W E R:
X= 28.2
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30 points
An airplane is climbing at an angle of
11° with the ground. Find, to the
nearest foot, the distance the airplane
has traveled when it has attained an
altitude of 400 feet.
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Answer
30 points
A N S W E R:
The plane has
gone 2,096 ft.
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40 points
A 10-foot ladder is to be placed against the
side of a building. The base of the ladder must
be placed at an angle of 72° with the level
ground for a secure footing. Find, to the
nearest tenth of a foot, how far the base of the
ladder should be from the side of the building
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40 points
A N S W E R:
3.1 feet
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The accompanying diagram
shows a flagpole that stands on
level ground. Two cables r & s
are attached to the pole at a point
16 feet Above the ground. The
combined length of the two cables
is 50 feet. If cable r is attached to
the ground 12 feet from the base
of the pole, what is the angle, x, to
the nearest degree, that the cable s
makes with the ground?
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50 points
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Answer
50 points
A N S W E R:
x  32 
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