Transcript The Escalator Problem

Trigonometry
Supplemental Questions
Problem 1
Jessica observed a mountain climber
reaching the summit, which is
known to be at 2,358 ft.
If Jessica is standing 1500 ft. from
the base, at what angle did she sight
the mountain climber to the nearest
degree?
What’s your strategy?
1.
Draw a figure to represent the
problem.
2.
Determine which trigonometric
ratio to use.
3.
Calculate the angle of
elevation.
1. Draw a figure to represent
the problem.
M
2,358 ft.
x°
S
1,500 ft.
C
2. Determine which trigonometric
ratio to use.
M
2,358 ft.
x°
S
1,500 ft.
Tangent
C
3. Calculate the Angle of Elevation.
Tan C° = MS
SC
Tan x° = 2,358 ft.
1,500 ft.
x = Tan-1 2,358 ft.
1,500 ft.
x = 57.538°
C≈ 58°
Problem 2
A rescue helicopter pilot sights
o
a life raft at a 26 angle of
depression. The helicopter is
3 km above the water.
What is the pilot’s distance
from the raft on the surface of
the water to the nearest km?
What’s your strategy?
1.
Draw a figure to represent the
problem.
2.
Determine which trigonometric ratio
to use.
3.
Calculate the surface distance.
1. Draw a figure to represent
the problem.
H
26°
3 km
26°
W
x km
R
2. Determine which trigonometric
ratio to use.
H
26°
3 km
26°
W
x km
Tangent
R
3. Calculate the surface distance.
Tan R° = HW
WR
Tan 26° = 3 km
x km
x (Tan 26°) = 3 km
x = 3 km
Tan 26°
x = WR ≈ 6.1509 km
Problem 3
Kevin is standing at the back of the cruise ship and
observes two sea turtles following each other,
swimming in a straight line in the opposite direction
of the ship. Kevin’s position is 206 meters above sea
level and the angles of depression to the two sea
turtles are 43° and 47°. Calculate the distance
between the two sea turtles to the nearest meter.
K
43° 47°
206 m
S
T
O
What’s your strategy?
1.
Separate and re-draw the two
triangles.
2.
Calculate individual horizontal
distances.
3.
Calculate the difference between
the two horizontal distances.
1. Separate and re-draw the two triangles.
43°
K
47°
206m
43°
S
K
206m
47°
x
O
T
y
O
2. Calculate individual horizontal distances.
Tan S° = KO
SO
Tan T° = KO
TO
Tan 43° = 206 m
x
Tan 47° = 206 m
y
x (Tan 43°) = 206 m
x (Tan 47°) = 206 m
x = 206 m
Tan 43°
x = 206 m
Tan 47°
x = 220.90795
x = 193.03062
SO = 220.90795 m
TO = 193.03062 m
3. Calculate the differences between the
two horizontal distances.
ST = SO – TO
ST = 220.90795 – 193.03062
ST = 27.8773
ST ≈ 28 m