Transcript 8.5 Notes - crunchy math
D.N.A.
1. Find the sin B, cos B, and tan B.
C
5 2. Find the value of
x
.
B
14
A
12
x C A
11 6
B
A
Find
x
. Round to the nearest tenth.
B
1) 45
x
2)
A
15 41
C
3)
A C
17
x
34
B C
15
x B
8 – 5: Angles of Elevation and Depression
pp. 464 - 470
• Solve problems involving angles of elevation.
• Solve problems involving angles of depression.
• angle of elevation • angle of depression
Standard 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
(Key)
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
Make a drawing
S
o:h
C
a:h
T
o:a
Tan 27
opp.
adj.
30
.
5
x = Opposite
.
5095 1
.
5095
x
30
.
5
x
30
.
5
x
30
.
5
.
5095 59
.
9
Adjacent =
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.
A B.
B C.
D.
C D
Make a drawing Diver = 6’
Platform height = 32’
S
o:h
C
a:h
T
o:a
Opp = 38’
Tan
x
opp.
adj.
Tan
x
0 .
8444 0 .
8391
m
x
40 38 45
Adj = 45’ Pool width = 50’
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 °
A.
B.
A B
B.
35 °
C.
C
C.
40 ° 0% 0% 0% 0%
D.
D
D.
50 ° A B C D
Angle of Depression
From her treehouse, Joan can look directly into her bedroom window. The angle of depression from the is 10 meters from the base of the house. How far is the treehouse from the base of the house?
Cos 42
adj.
hyp
adj.
Cos 42
10
x x
10
cos 42
10
.
7431 13
.
5
m hyp.
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.
Sin A
0.3 cm
6
B
31.4 cm
opp
0
.
1045
hyp C
31.5 cm
x
3
3
(.
D
298.4 cm 1045
)
x
3
3
Opposite x
Multiply each side by 3.
Answer:
Simplify.
The height of the ramp is about 0.314 meters, or 0.314(100) = 31.4 centimeters. The answer is B.
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
A B C D
• Homework: • pp 466 – 470, problems 1 – 10, 27, and 29 – 35
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.
x
35
154
Indirect Measurement
Δ
MLK
and Δ
MLJ
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
m
MJL
36
and
m
MKL
35
.
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.
x
35
154
154 x
35
Tan 35
154
x
.
7002 154
x x
154
.
7002 219
.
94
m
219.94m
x m
154 y
36
154 y
36
Tan 36
154
y
.
7265 154
y y
154
.
7265 211
.
98
m
219.93 m 211.98 m
Answer:
The distance between the dolphins is
JK
–
JL
–
KL
≈ 219.93 – 211.96
, KL.
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 two cars to the nearest foot.
1.
A 2.
B
A.
14 ft
3.
C
B.
24 ft
4.
D
C.
D.
37 ft 49 ft A B C D