Transcript Section 6.1 - Shelton State Community College

Section 6.1
The Law of Sines
Overview
• In this chapter we exploring solving triangles
that are not right triangles.
• SOH-CAH-TOA does NOT work on triangles
that are not right triangles!!!!
• Neither does the Pythagorean Theorem!!
Some important information
• The sum of the angles in any triangle is 180
degrees.
• The sides and angles are in proportion—the
longer the side, the larger the angle opposite
that side.
The Law of Sines
sin A sin B sin C


a
b
c
Examples
1. C = 41°, B = 68°, a = 14
2. A tower leans at an angle of 84.7°. At a
distance of 165 feet from the base of the
tower, the angle of elevation to the top is
51.0°. Find the distance, to the nearest foot,
from the base to the top of the tower.
The Ambiguous Case
• Possible when given two sides and an angle
opposite one of those sides.
• One triangle, two triangles, or no triangle at
all.
• Assume that there are two triangles, then look
for a contradiction.
Examples
1. a = 7, b = 4, A = 30°
2. a = 11, b = 29, A = 30°
3. a = 12, b = 14.7, A = 40°
Area of a triangle
1
A  bc sin A
2
1
A  ac sin B
2
1
A  ab sin C
2
Examples
• Find the area of each triangle below:
1. B = 35°, a = 17 feet, c = 38 feet
2. B = 41°, a = 3 yards, c = 5 yards