1. 8-5 The Law of Sines
Geometry

2. Triangles without a right angle
To solve a triangle with no right angle, you need to know the measure of at least one side and any two other parts of the triangle.

3. 4 possible cases LAW OF SINES AAS or ASA (Two angles and any side)
SSA (Two sides and an angle opposite one of them)
LAW OF COSINES
SSS (Three sides)
SAS (Two sides and their included angle)

4. Law of Sines
If has sides of length a, b, and c as shown, then B A C

5. Ex. 1
Use a calculator to find each trig. Ratio. Round to the nearest hundredth. 1a) tan 103° 1b) cos 165° 1c) sin 93°

6. Ex. 2
Find AC. Round lengths to the nearest tenth. A C 18 B
44°
67°

7. Ex. 3
Find each measure . Round lengths to the nearest tenth and angle measures to the nearest degree. F G 3a) FG 40 H 3b) m∠Q 6 P R 8 Q
39°
32°
51° 51

8. Assignment

9. 8-5B Law of Cosines

10. Ex. 4
The distance from Mercury to the sun is about 36 million miles. The distance from Earth to the sun is about 93 million miles. Estimate the distance from Earth to Mercury if the observed angle between the sun and Mercury is 19 degrees.

11. SSA Case
2 sides & an angle opposite one of the sides (SSA) may determine no triangle, one triangle, or two triangles.

12. Possible Triangles in the SSA Case
A is OBTUSE A is ACUTE

13. Area of a Triangle
The area of any triangle is given by one half the product of the lengths of two sides times the sine of their included angle.

14. Ex. 4
Find the area of B
10 in.
A C
#7 Guided practice pg. 885