SOLUTION: Find the area of Triangle ABC, if AB=6cm, AC=12cm, and the measure of angle A is 20 degrees. Express your answer to the nearest tenth of a square centimeter.
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Question 442956: Find the area of Triangle ABC, if AB=6cm, AC=12cm, and the measure of angle A is 20 degrees. Express your answer to the nearest tenth of a square centimeter. Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website! We know that angle A is opposite BC.
Let's call side AB and side AC
We can find what cos(A) is since we know A = 20º
Let's use the law of cosines.
Let BC = a, AB = c , AC = b
a^2 = b^2 + c^2 - 2bc cos(20)
a^2 = 12^2 + 6^2 - 2(12)(6)cos(20)
a^2 = 144 + 36 - (144cos(20)
a^2 = 180 - 144*cos(20º)
Use your calculator find cos(20º). Make sure your calculator is in DEGREE MODE and not RADIAN MODE.
a^2 = 180 - 144 * (0.939692621)
a^2 = 44.6842626
a = 6.68462883
We know that (1/2)(a)(b) gives us the area.
We have a and we have b.
(1/2)(6.68462883)(6) = 20.053888565 cm.
cm when rounded.
