Title: 7.6 Law of Sines
17.6 Law of Sines
2Objective
- Use the Law of Sines to solve triangles and
problems
3Law of Sines
- In trigonometry, we can use theLaw of Sines to
find missing parts of triangles that are not
right triangles. - Law of Sines In ?ABC, sin A sin B sin
C a b c
4Example 1a
Find p. Round to the nearest tenth.
5Example 1a
Law of Sines
Cross products
Use a calculator.
6Example 1b
Law of Sines
Cross products
Divide each side by 7.
7Example 1b
Solve for L.
Use a calculator.
8Your Turn
a. Find c. b. Find m?T to the nearest
degree in ?RST if r 12, t 7, and m?R 76.
9Solving a Triangle
- The Law of Sines can be used to solve a
triangle, which means to find the measures of
all of the angles and all of the sides of a
triangle.
10Example 2a
11Example 2a
Angle Sum Theorem
Add.
Subtract 120 from each side.
12Example 2a
To find d
Law of Sines
Substitute.
Cross products
Divide each side by sin 8.
Use a calculator.
13Example 2a
To find e
Law of Sines
Substitute.
Cross products
Divide each side by sin 8.
Use a calculator.
14Example 2b
We know the measure of two sides and an angle
opposite one of the sides.
Law of Sines
Cross products
15Example 2b
Divide each side by 16.
Solve for L.
Use a calculator.
Angle Sum Theorem
Substitute.
Add.
Subtract 116 from each side.
16Example 2b
Law of Sines
Cross products
Use a calculator.
17Your Turn
18Example 3
19Example 3
20Example 3
Law of Sines
Cross products
Use a calculator.
Answer The length of the shadow is about 75.9
feet.
21Your Turn
A 5-foot fishing pole is anchored to the edge of
a dock. If the distance from the foot of the pole
to the point where the fishing line meets the
water is 45 feet, about how much fishing line
that is cast out is above the surface of the
water?
Answer About 42 feet of the fishing line that
is cast out is above the surface of the water.
22Assignment
- Pre-AP Geometry Pg. 381 15, 16 32 evens, 42
- Geometry Pg. 381 15, 16 28 evens