section 14.4. 1. to find the area of any given triangle by using trig functions (sine) 2. to use...
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Section 14.4
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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
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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.
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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
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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
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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.
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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.