MATH 117
Right Triangle Problems
Part 2
1. A 50 ft pole has a support wire that runs from its top to the ground with an angle of
depression of 75º 48’. (a) Illustrate and label the situation.
! = 75. 8º
Ang. of Depression
50
ft
w
! = 75. 8º
b
(b) How far from the base of the pole does
the wire connect to the ground?
tan(75.8º ) =
b=
(ii) How much wire is used?
sin(75.8º ) =
50
b
50
" 12.65 ft
tan(75.8º )
w=
!
50
w
50
" 51.58 ft
sin(75.8º )
!
!
!
2. A 6 foot pole rises from the ground. The top of the pole is 8 inches off of vertical.
(a) Solve for the angle of lean. (b) How high off the ground is the top of the pole?
8"
h
$ 8 /12 ft '
" = sin#1&
) * 6.38º
% 6 ft (
6 ft
pole
!
In inches,
h = 72 2 " 8 2 # 71.55 in.
! Angle of Lean
3. (a) An adjustable ramp is 14 ft long and
rises 4 ft off the ground. Solve for
the angle of elevation.
14 ft
!
(b) If the angle of elevation is adjusted to
23º 24’, then how high will the ramp
rise off the ground?
14 ft
4 ft
!
! = 23. 4 º
" = sin#1 (4 /14) $ 16.6º
!
h
h = 14 sin(23.4º ) " 5.56 ft
!
4. At a certain distance, the angle of elevation to the top of a building is 60º. From 50
feet further back, the angle of elevation is 40º. Solve for the height of the building.
tan(60º ) =
h
x
and
tan(40º ) =
h
50 + x
So,
h
!
h = x tan(60º )
!
and h = (50 + x)tan(40º )
Thus, x tan(60º ) = (50 + x)tan(40º ) .
x first, then substitute x into
We solve for !
h = x tan(60º ) to get h .
!
!
60º
40º
x
50 ft
x tan(60º ) = 50tan(40º ) + x tan(40º ) "
!
" x=
!
50tan(40º )
(tan(60º ) " tan(40º ))
!
"
!
!
x!
)
(tan(60º!) " tan(40º )) = 50tan(40º
50tan(40º )tan(60º )
h = x " tan(60º ) =
$ 81.38 ft
tan(60º ) # tan(40º ))
(
!
!
!
!
5. A building is 100 ft high. From a distance at point A on the gound, the angle of
elevation to the top of the building is 30º. From a little nearer at point B, the angle of
elevation is 40º. Solve for the distance from point A to point B.
tan(40º ) =
100
ft!
30º
40º
A d B
x
Finally, d =
!
100
100
ft
so x =
tan(40º )
x
100
Then, tan(30º ) =
d+ x
!
So
100
d+ x=
!
tan(30º )
100
100
100
"x=
"
# 54 ft
!
tan(30º )
tan(30º ) tan(40º )