Geometry
Name_________________________
Date _______________
DAY 7 WARM UP
1. The angle between the bottom of a fence and the top of a tree is 75°.
The tree is 4 feet from the fence. How tall is the tree? Round your answer
to the nearest foot.
x
75°
4 ft
Find the value of x to the nearest tenth.
2.
x
38
3.
25
x
10
20
Classify each angle as an angle of elevation or an angle of depression.
4.
5.
6. Find the value of each variable.
w
z
45
160
30
Day 7
Today, we will understand how to solve for all angles and sides in a right triangle.
At the end of today, you will be able to find all side lengths and angles using trigonometric ratios.
Solving Right Triangles
to solve a right triangle –
you must know either:
- two side lengths
- one side length and one acute angle
B
Inverse Trigonometric Ratios
inverse sine - If sin A = x, then sin-1 x = m  A
inverse cosine - If cos A = y, then cos-1 y = m  A
inverse tangent - If tan A = z, then tan-1 z = m  A
C
A
Examples
1. Use a calculator to approximate the measure of  A to the nearest tenth of a degree. Then find  C.
C
15
B
20
A
2. Let  A and  B be acute angles in a right triangle. Use a calculator to approximate the measures of
 A and  B to the nearest tenth of a degree.
a. sin A = 0.87
b. cos B = 0.15
c. tan A = 0.24
d. sin B = 0.56
3. Solve the right triangle. Round decimals to the nearest tenth.
A
42
70 ft
C
B
4. Solve the right triangle. Round decimals to the nearest tenth.
G
14
H
16
J
5. Solve the right triangle. Round decimal answers to the nearest tenth.
B
26
A
4.5
C
6. The angle of elevation from a point 25 feet from the base of on a level ground to the top of the tree is
30°. Find the height of the tree.
Worksheet – Practice solving right triangles
Solve the right triangle. Round decimal answers to the nearest tenth.
1.
2.
P
22
N
18
11
P
37
Q
3.
Q
R
U
4.
V
M
14
T
23
51
7
D
S
Let A be an acute angle in a right triangle. Approximate the measure of A to the nearest tenth of
a degree.
5. sin A = 0.36
6. tan A = 0.8
7. sin A = 0.27
8. cos A = 0.35
9. A dead tree was struck by lightning, causing it to fall over at a point 10 feet up from its base. If
the fallen treetop forms a 40° angle with the ground, how tall was the tree originally to the nearest
foot?