1. Area and the Law of Sines
Section 14.4

2. Objectives… 1. To find the area of any given triangle by
using trig functions (sine)
2. To use the Law of Sines in finding side
lengths and angle measurements of non-
right triangles

3. Finding the Area of a Triangle
you can find the area of any oblique (non-right) triangle if you have any two side measurements and the “included angle” (angle in between)
formula: (1/2)*(product of two side measurements)*(sin of given angle)
Example 1: A triangle has sides of lengths 12 in. and 15 in., and the measure of the angle between them is 24°. Find the area of the triangle.

4. The Law of Sines
The “Law of Sines” describes algebraically the relationship between the lengths of the sides of any triangle and the sine values of the angles opposite them

5. When can you use this law?
You can use the “Law of Sines” to find missing measures (side and/or angle) of any triangle when you have the following:
A. the measurements of two angles and any
side or
B. the lengths of two sides and the angle
opposite one of them

6. Examples… A. Given triangle KLM, m∠K = 120°,
m∠M = 50°, and ML = 35 yd. Find KL.
B. Given triangle PQR, m∠R = 97.5°,
r = 80 ft., and p = 75 ft. Find m∠P.
C. Given triangle ABC, m∠A = 33°, m∠C =
64°, and BC = 8 cm. Find AC.

7. More Examples… D. Given triangle XYZ, x = 7 in., y = 10 in.,
and m∠Y = 98°. Find m∠Z.
E. Given triangle TUV, m∠T= 28°, t = 8.5 m.,
and v = 13.5 m. Find all remaining
unknown measures.
F. Given triangle DEF, m∠D = 43°,
e = 15 mm., and f = 20 mm. Find m∠E.