Section 14.4

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

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.

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

sin sin sinA B C

a b c

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

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.

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.