Aim #26: Trigonometric Word Problems
CC Geometry R
Do Now: Solve for x in the accompanying diagrams.
• What is the same about how the angle of elevation and angle of depression are
formed?
The angle of elevation
or depression is the
angle between the
horizontal (parallel to
the Earth;s surface) and
the line of sight.
• What do you notice about the measure of the angle of depression and the
angle of elevation?
Why?
Exercise (1): The angle of elevation from a point on a gym floor to the top of a
0
rope ladder hanging from the ceiling is 40 . The distance from the same point on
the floor to the base of the ladder is 30 feet. How long is the ladder, to the
nearest tenth of a foot?
Exercise (2)
Scott, whose eye level is 1.5 m above the ground, stands 30 m from a tree. The
0
angle of elevation of a bird at the top of the tree is 36 . How far above the
ground is the bird? Round answer to the nearest tenth.
Exercise (3):
Standing on his rooftop, John's watches his friend approach his building. John's
0.
angle of depression from his eye level is 40 The rooftop is 16 m above the
ground, and John's eye level is 1.8 m above the rooftop. What is the distance
between John's friend and the building, to the nearest tenth of a meter?
Exercise (4)
Standing on the gallery of a lighthouse (the deck at the top of a lighthouse), a
0
person spots a ship at an angle of depression of 20 . The lighthouse is 28 m tall
and sits on a cliff 45 m tall as measured from sea level. What is the horizontal
distance, to the nearest meter, between the lighthouse and the ship? Sketch a
diagram and show work.
5) Johanna wants to build a fence around the corner space of her backyard to
prevent her dog from digging up the seeds that she plants. Shedecided that she
could just use the Pythagorean theorem to find the length of the fence she‛d need.
a) Is the Pythagorean theorem applicable in this situation? Explain.
b) How can Johanna figure out the length of the fence? Round your answer to
the nearest hundredth.
6) The measurements of the triangle shown below are rounded to the nearest
hundredth. Calculate the missing side length to the nearest hundredth.
x
Cos 42 = 21
x = 15.6060
y
Cos 38 = 18.08
y = 14.2472
x + y = 29.85
x
21
y
110o
38o
18.08