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8-3 Solving Right Triangles
Holt Geometry
8-3 Solving Right Triangles
In Short,
To find a ratio or missing side length
use Sin, Cos, Tan
To find the angle use sin-1, Cos-1, Tan-1
Holt Geometry
8-3 Solving Right Triangles
Example 2: Calculating Angle Measures from
Trigonometric Ratios
Use your calculator to find each angle measure
to the nearest degree.
A. cos-1(0.87)
B. sin-1(0.85)
C. tan-1(0.71)
cos-1(0.87)  30°
sin-1(0.85)  58°
tan-1(0.71)  35°
Holt Geometry
8-3 Solving Right Triangles
Example 3: Solving Right Triangles
Find the mR. Round angle
measures to the nearest degree.
Holt Geometry
8-3 Solving Right Triangles
Example 4: Solving a Right Triangle in the Coordinate
Plane
The coordinates of the vertices of ∆PQR are
P(–3, 3), Q(2, 3), and R(–3, –4). Find the side
lengths to the nearest hundredth and the
angle measures to the nearest degree.
Holt Geometry
8-3 Solving Right Triangles
Example 4 Continued
Step 1 Find the side lengths. Plot points P, Q, and R.
PR = 7
Y
P
By the Distance Formula,
Q
X
R
Holt Geometry
PQ = 5
8-3 Solving Right Triangles
Example 4 Continued
Step 2 Find the angle measures.
Y
P
mP = 90°
Q
X
R
The acute s of a rt. ∆ are comp.
mR  90° – 54°  36°
Holt Geometry
8-3 Solving Right Triangles
An angle of elevation is the angle formed by a
horizontal line and a line of sight to a point above
the line. In the diagram, 1 is the angle of elevation
from the tower T to the plane P.
An angle of depression is the angle formed by a
horizontal line and a line of sight to a point below
the line. 2 is the angle of depression from the
plane to the tower.
Holt Geometry
8-3 Solving Right Triangles
Example 1A: Classifying Angles of Elevation and
Depression
Classify each angle as an
angle of elevation or an
angle of depression.
1
It is an angle of depression.
4
It is an angle of elevation.
Holt Geometry
8-3 Solving Right Triangles
Use the diagram above to
classify each angle as an
angle of elevation or
angle of depression.
1a. 5
It is an angle of depression.
1b. 6
It is an angle of elevation.
Holt Geometry
8-3 Solving Right Triangles
Check It Out! Example 2
What if…? Suppose the plane is at an altitude of
3500 ft and the angle of elevation from the airport to
the plane is 29°. What is the horizontal distance
between the plane and the airport? Round to the
nearest foot.
You are given the side opposite
A, and x is the side adjacent to
A. So write a tangent ratio.
Multiply both sides by x and
divide by tan 29°.
x  6314 ft
Simplify the expression.
29°
Holt Geometry
3500 ft
8-3 Solving Right Triangles
Check It Out! Example 3
What if…? Suppose the ranger sees another fire
and the angle of depression to the fire is 3°. What
is the horizontal distance to this fire? Round to the
nearest foot.
3°
By the Alternate Interior Angles Theorem, mF = 3°.
Write a tangent ratio.
x  1717 ft
Holt Geometry
Multiply both sides by x and
divide by tan 3°.
Simplify the expression.