Section 2 – Right Triangle Trigonometry
Word Problems
A surveyor is standing 50 feet from the base of a large tree. The
surveyor measures the angle of elevation to the top of the tree as
71.5. How tall is the tree?
x
tan71.5 
50
x  149.434 ft.
X
71.5
50
A 40-foot flagpole casts a 30 foot shadow. Find the angle of
elevation of the sun.
40
tan  
30
  53.130
40

30
From a point 50 feet away from the entrance to Lincoln-Way East,
Yugo measured the angle of elevation to the top of the building to
be 16 . How tall is the building?
x
tan16 
50
x  14.337
X
50
16
Pat wanted to measure the height of the flagpole at Lincoln-Way
East. From a point, he measured the angle of elevation of the
flagpole to be 63 . He then moved back 15 feet and found the
angle of elevation from there to be 42. How tall is the flagpole?
x
tan63 
y
x
y
tan63
x
tan42 
y  15
x
tan 42 
x
 15
tan63
X
42
15
63
y
tan 42 
x
x
 15
tan63
24.955 feet
A student looks out a second-story window and sees the top of the
flagpole at an angle of elevation of
. 22
The student is 18 feet
above the ground and 50 feet from the flagpole. Find the height of
the flagpole.
x
tan 22 
50
x  20.201
20.201  18  38.201 feet
X
22
18
50
From points A and B, 10 feet apart, the angle of elevation of the
top of a tower are 40 and 54 . Find the tower’s height.
tan54 
x
y
x
y
tan54
x
tan40 
y  10
tan 40 
x
x
 10
tan54
X
40 10
A
54
B
y
tan 40 
x
x
 10
tan54
X = 21.496 feet