Download Unit 0 PPT 4.1 Applied Right Triangle Trig Part 1

Unit 0 4.1 Applied Right
Triangle Trigonometry Part 1
OBJ: SWBAT solve application problems
involving right triangle trigonometry
HW: p 259 (52-56, 58)
Vocabulary

Angle of Depression
and Angle of
Elevation are Equal
Horizontal Line
Angle of Depression
Angle of Elevation
Horizontal Line
#1 Identifying Angles of
Elevation and Depression
1 is the angle of depression
2 is the angle of elevation
1
2
#2 Real-World Connection

You sight a rock climber on a cliff at a 32o
angle of elevation. The horizontal ground
distance to the cliff is 1000 ft. Find the line of
sight distance to the rock climber.
1000
Cos 32 
x
1000
x
Cos 32
x  1179 ft
x
32
1000 ft
#3 Real-World Connection

An airplane pilots sights a life raft at a 26o
angle of depression. The airplane’s altitude is
3 km. What is the airplane’s surface distance
d from the raft?
3
Tan 26 
d
3
d
Tan 26
d  6.2 km
26
3 km
26
d
Finding the Bearing



Navigation involves using direction or bearing.
Bearings are given as angles rotated from the north
or south.
In the figure below, O represents the center of the
earth.
Bearing from O to A is N30ºE.
Bearing from O to B is N60ºW.
Bearing from O to C is S70ºE.
Bearing from O to D is S80ºW.
Ex 4) Finding the bearing of an airplane

A Boeing 777 aircraft takes off
from O’Hare Airport on runway 2
LEFT, which has a bearing of
N20ºE. After flying for 1 mile, the
pilot requests permission to turn
90º northwest. The request is
granted.

After the plane goes 2 miles in
this direction, what bearing should
the control tower use to locate the
aircraft?
Ex 4) Continued
2
tan    2
1
  tan 1 (2)
  63.4o
To find the bearing the control tower
must use to locate the aircraft, we
need to find the acute angle
between north and the ray OQ.
63.4o  20o  43.4o
The bearing of the aircraft from O to Q is N43.4oW.