Download 8-6 Law of Sines - Ms. Fowls` Math Classes

8-6 Law of Sines
 The Law of Sines can be used to find missing parts of
triangles that are not right triangles.
 Theorem 8.8: Let ∆ABC be any triangle with a, b,
and c representing the measures of the sides
opposite the angles with measures A, B, and C,
respectively. Then sin A sin B sin C


a
b
c
B
c
a
A
b
C
Video Link
Law of Sines
Let’s review the Proof for the Law of
Sines on page 471.
 Example 1
 A: If m∠B = 32, m∠C = 51, c = 12, find a.
sin A sin C 180  (32  51)  97  mA sin 97 sin 51


a
c
a
12
a  15.3
12(sin 97)
a
sin 51
 Example 1
 B: If a = 22, b = 18, m∠A = 25, find m∠B.
sin A sin B sin 25 sin B sin 25
(18)  sin B


22
22
18
a
b
 sin 25

sin 1 
(18)   B
 22

20  B
Example 2
 Solving a Triangle: Finding the measures of
all of the angles and sides of a triangle.
 Find the missing angles and sides of ∆PQR.
Round angle measures to the nearest degree
and side measures to the nearest tenth.
 A: m∠R = 66,m∠Q = 59,p = 72
 Answer: m∠P = 55, q ≈ 75.3, r ≈ 80.3
 B: p = 32, r = 11, m∠P = 105
 Answer: m∠R = 19, m∠Q = 56, q = 27.5
Video Link
Law of Sines – Missing Side
Example 3
 Two radar stations that are 35 miles apart
located a plane at the same time. The first
station indicated that the position of the plane
made an angle of 37° with the line between
the stations. The second station indicated
that it made an angle of 54° with the same
line. How far is each station from the plane?
 Draw a picture – label the parts – use law of
sines to find the missing pieces.
 Answer: about 21.1 mi, about 28.3 mi
Key Concepts
 The Law of Sines can be used to solve a
triangle in the following cases.
 Case 1: You know the measures of two angles
and any side of a triangle. (AAS or ASA)
 Case 2: You know the measures of two sides
and an angle opposite one of these sides of
the triangle. (SSA)
 Handout – Extra Examples for additional
understanding.
Homework #54
 p. 475 13-29 odd, 34, 38-39