Download Solving Right Triangles To solve a right triangle

Sect. 9.6 Solving Right
Triangles
Goal 1
Solving a Right Triangle
Goal 2
Using Right Triangles in Real
Life
Solving Right Triangles
To solve a right triangle:
• Means to determine the measures
of all six parts of the triangle
You can solve a right triangle if
you know either of the following:
•Two side lengths
•One side length and one acute
angle measure
Solving Right Triangles
You can use the side lengths of a right triangle to
find trigonometric ratios for the acute angles.
• Once you know the sine, cosine, or tangent of
an acute angle, you can use a calculator to find
the angle.
For an acute angle A:
• If sin A = x, then sin-1 x = m A
(sin-1 x is read “the inverse sine of x)
• if cos A = x, then cos-1 x = m A
• if tan A = x, then tan-1 x = m A
Solving Right Triangles
Example 1
Find the measure of each angle given the following
trig functions
a) sin A = .3846
b) cos B = .6560
c) tan C = .26794
1
d) cin D =
2
3
e) cos E =
16
Solving Right Triangles
Example 2
B
Solve the right triangle.
Round decimals to the
nearest tenth.
10
8
A
b
C
Solving Right Triangles
Example 3
Solve the triangle.
Round decimals to the
nearest tenth.
S
15
r
20°
T
s
R
Solving Right Triangles
Example 4
Solve the right triangle.
Round decimals to the
nearest tenth.
A
b
C
12
10
B
Using Right Triangles in Real Life
Example 5
During a flight, a hot air balloon is
observed by two persons standing at
points A and B as shown in the diagram.
The angle of elevation of point A is 28°.
Point A is 1.8 miles from the balloon as
measured along the ground.
a) What is the height h of the balloon?
h
28°
B
1.8 mi.
2.8 miles
Tan 28 h

1
2.8
b) Point B is 1.8 miles from the balloon at ground level. Find the angle
of elevation of point B.
1.49
tan B 
1.8
A
Using Right Triangles in Real Life
Example 6
At a Certain time, a
vertical pole 3 m. tall
cast a 4 m. shadow.
What is the angle of
elevation of the sun?
3 m.
4 m.
Homework
9.6 10-32 even, 34-38, 47-55
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