Download Law of Sines

Trigonometric Ratios 14-3, 14-4, 14-5
Name __________________________ Per. ______
• To determine whether to use the Law of Sines or the Law of Cosines, look at
the given information.
• If given the measure of two sides for a triangle and the angle between them or
the measure of all three sides, use the Law of Cosines.
• If given the measure of two angles of a triangle and the length of any side or
the measure of two sides and the measure of the angle opposite one of them,
use the Law of Sines.
Law of Sines: sin A  sin B  sin C
a
b
c
Use the Law of Sines when you are given the measure of two angles of a triangle and the
length of any side or the measure of two sides and the measure of the angle opposite one of
them.
5. Find a if A = 18, B = 28, and b = 100.
6. Find c if B = 18, C = 152, and b = 4.
7. Find a if C = 16°, A = 92, and c=5 32.
8. Find B if C = 95, b = 5, and c = 6.
9. Find B if A = 40, b = 6, and a = 12.
11. Find c if B = 110, C = 40, and b = 18.
Law of Cosines
In  ABC,
a is the length of the side opposite A,
b is the length of the side opposite B, and
c is the length of the side opposite C.
a2 = b2 + c2 –2bc cos A
b2 = a2 + c2 –2ac cos B
c2 = a2 + b2 –2ab cos C
10. Find c if A = 50, C = 60, and a = 36.
12. Find a if A = 5, C = 125, and c = 510.
• Use the Law of Sines or Law of Cosines. Find the measure x to the nearest tenth.
• 31.
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4. Find a if A = 18°, c = 72, and b = 100.
5. Find A if B = 45°, a = 9, and c = 19.
6. Find B if a = 9, b = 3, and c = 11.
7. Find C if B = 95°, a = 5, and c = 6.
8. Find c if a = 15, C = 152°, and b = 4.
9. Find a if A = 16°, b = 92, and c = 32.
10. Find c if C = 30°, a = 15, and b = 15.
11. Find B if a = 18, b = 26, and c = 15.
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