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1. Use a graphing calculator to find tan 54°. Round to the
nearest ten-thousandth.
2. Find mB to the nearest tenth of a degree if
cos B = 0.8926 and B is an acute angle.
3. Refer to the figure. Find the value
of x to the nearest tenth.
4. Refer to the figure. Find the value
of x to the nearest tenth.
• Solve problems involving angles of elevation.
• Solve problems involving angles of depression.
• angle of elevation
• angle of depression
Angle of Elevation
CIRCUS ACTS At the circus, a person in the
audience at ground level watches the high-wire
routine. A 5-foot-6-inch tall acrobat is standing on a
platform that is 25 feet off the ground. How far is the
audience member from the base of the platform, if the
angle of elevation from the audience member’s line of
sight to the top of the acrobat is 27°?
Make a drawing
Angle of Elevation
Since QR is 25 feet and RS is 5 feet 6 inches or 5.5 feet,
QS is 30.5 feet. Let x represent PQ.
Multiply both sides by x.
Divide both sides by tan
Simplify.
Angle of Elevation
Answer: The audience member is about 60 feet from
the base of the platform.
DIVING At a diving competition, a 6-foot-tall diver
stands atop the 32-foot platform. The front edge of
the platform projects 5 feet beyond the ends of the
pool. The pool itself is 50 feet in length. A camera is
set up at the opposite end of the pool even with the
pool’s edge. If the camera is angled so that its line of
sight extends to the top of the diver’s head, what is
the camera’s angle of elevation to the nearest
degree?
A. 37°
B. 35°
C. 40°
D. 50°
A.
B.
C.
D.
A
B
C
D
Angle of Depression
A wheelchair ramp is 3 meters long and inclines at 6°.
Find the height of the ramp to the nearest tenth of a
centimeter.
A 0.3 cm
B 31.4 cm C 31.5 cm D 298.4 cm
Read the Item
The angle of depression between the ramp and the
horizontal is
Use trigonometry to find the height of
the ramp.
Solve the Item
Method 1
The ground and the horizontal level with the platform
to which the ramp extends are parallel. Therefore,
since they are alternate interior
angles.
Angle of Depression
Multiply each side by 3.
Simplify.
Answer: The height of the ramp is about 0.314 meters,
or 0.314(100) = 31.4 centimeters. The answer
is B.
Angle of Depression
Method 2
The horizontal line from the top of the platform to which
the wheelchair ramp extends and the segment from the
ground to the platform are perpendicular. So,
and
are complementary angles. Therefore,
Angle of Depression
Multiply each side by 3.
Simplify.
Answer: The height of the ramp is about 0.314 meters,
or 0.314(100) = 31.4 centimeters.
A roller coaster car is at one of its highest points. It
drops at a 63° angle of depression for 320 feet. How
long of a vertical distance was the drop?
A. 145 ft
B. 628 ft
C. 359 ft
D. 285 ft
1.
2.
3.
4.
A
B
C
D
Indirect Measurement
Vernon is on the top deck of a cruise ship and
observes two dolphins following each other directly
away from the ship in a straight line. Vernon’s
position is 154 meters above sea level, and the
angles of depression to the two dolphins are 35° and
36°. Find the distance between the two dolphins to
the nearest meter.
Indirect Measurement
ΔMLK and ΔMLJ are right triangles. The distance
between the dolphins is JK or JL – KL. Use the right
triangles to find these two lengths.
Because
are horizontal lines, they are parallel.
Thus,
and
because they
are alternate interior angles. This means that
Indirect Measurement
Multiply each side by JL.
Divide each side by tan
Use a calculator.
Indirect Measurement
Multiply each side by KL.
Divide each side by tan
Use a calculator.
Answer: The distance between the dolphins is JK – KL.
JL – KL ≈ 219.93 – 211.96, or about 8 meters.
Madison looks out her second-floor window, which is
15 feet above the ground. She observes two parked
cars. One car is parked along the curb directly in
front of her window, and the other car is parked
directly across the street from the first car. The
angles of depression of Madison’s line of sight to the
cars are 17° and 31°. Find the distance between the
1.
A
two cars to the nearest foot.
A. 14 ft
B. 24 ft
C. 37 ft
D. 49 ft
2.
3.
4.
B
C
D