10-6B
Finding Angle Measures plus
Angles of Elevation and
Depression
• Algebra 1
To find an angle measure, use
the inverse
• If you know the lengths of 2 sides of a right
triangle, then you can find a trigonometric
ratio for each acute angle of the triangle.
• If you know a trig ratio for an angle, you
can use the inverse of the trig ratio to find
the measure of the angle.
• Use the inverse sin, cos, or tan feature on
your calculator located above those
buttons.
Ex. 1a
In a right triangle,
The side opposite
 A is 8 mm long
and the hypotenuse
is 12 mm long.
What is the
measure of  A .

Ex. 1b

x

6
11
Vocabulary

Angle of Depression
and Angle of
Elevation are Equal
by AIA Thm because
horizontal lines are ll.
Horizontal Line
Angle of Depression
Angle of Elevation
Horizontal Line
Ex. 2 Identifying Angles of
Elevation and Depression
1 is the angle of depression
2 is the angle of elevation
1
2
Ex. 3 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
x
1000
x
Cos 32
x  1179 ft
32
1000 ft
Ex. 4) 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