5-4
Applying Trigonometric Functions
If J=50° and j=12, find r.
G
12
Sin 50⁰=12/r
.7660=12/r
.7660r=12
r=15.67
r
50°
R
g
J
If the angle that the rope makes with
the level ground is 52°15’, how long is
the rope?
The chair lift at a ski resort rises at an
angle of 20.75° and attains a vertical
height of 1200 feet.
1200
d
20.75°
• How far does the chair
lift travel up the side of
the mountain?
• sin 20.75°=1200/d
• .3543=1200/d
• .3543d=1200
• d=3387.0 ft
--------------------------------d
1200
20.75°
• A film crew in a helicopter records an overhead
view of a skier’s downhill run from where she
gets off the chair lift at the top to where she gets
back on the chair lift for her next run. If the
helicopter follows a level flight path, what is the
length of that path.
• About 3167.3 ft
• A regular pentagon is inscribed in a
circle with diameter 8.34
centimeters. The apothem of a
regular polygon is the measure of a
line segment from the center of the
polygon to the midpoint of one of its
sides. Find the apothem of the
pentagon.
The measure of α is
360⁄ 10 or 36°
• A regular hexagon is inscribed in a circle
with diameter 26.6 centimeters. Find the
apothem of the hexagon.
• About 11.5 cm
Angle of elevation – the angle between a horizontal line
and the line of sight from an observer to an object at a
higher level.
Angle of depression – angle to an object at a lower
angle.
• An observer in the top of a lighthouse
determines that the angles of depression to
two sailboats directly in line with the
lighthouse are 3.5° and 5.75°. If the observer
is 125 feet above sea level, find the distance
between the boats.
125
• John wants to measure the height of a tree.
He walks exactly 100 feet from the base of the
tree and looks up. The angle from the ground
to the top of the tree is 33º . How tall is the
tree?
• A building is 50 feet high. At a distance away
from the building, an observer notices that
the angle of elevation to the top of the
building is 41º. How far is the observer from
the base of the building?
• An airplane is flying at a height of 2 miles
above the ground. The distance along the
ground from the airplane to the airport is 5
miles. What is the angle of depression from
the airplane to the airport?
• A bird sits on top of a lamppost. The angle of
depression from the bird to the feet of an
observer standing away from the lamppost is .
The distance from the bird to the observer is
25 meters. How tall is the lamppost?
• A man who is 2 m tall stands on horizontal
ground 30 m from a tree. The angle of
elevation of the top of the tree from his eyes
is 28˚. Estimate the height of the tree.
• From a point 80 meters from the base of a
building to the top of the building the angle of
elevation is 51°. From the same point to the
top of a flag staff on the building the angle of
elevation is 54°.