SOLUTION: What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. unitsē A triangle with vertices labe

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Question 1085099: What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

unitsē
A triangle with vertices labeled as A, B, and C. Side B C is the base and the top vertex is A. Side A C is labeled as 15. Side A B is labeled as 12.5. Angle C A B is labeled as 77 degrees.
Found 3 solutions by Fombitz, ikleyn, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the law of cosines,
BC%5E2=12.5%5E2%2B15%5E2-2%2812.5%29%2815%29cos%2877%29
BC%5E2=381.25-375%280.22495%29
BC%5E2=296.8934
BC=17.23059
So then using the law of sines,
17.23059%2Fsin%2877%29=15%2Fsin%28b%29
sin%28b%29=0.8482326
b=58.02
So then,
h=12.5sin%2858.02%29
h=10.603
and
A=%281%2F2%29%28BC%29h
A=%281%2F2%29%2817.23059%29%2810.603%29
A=91.35

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The area of any and each triangle is half of the product of the measures of two its sides and the sine of the angle between these sides.

Area = %281%2F2%29%2A15%2A12.5%2Asin%2877%5Eo%29.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

unitsē
A triangle with vertices labeled as A, B, and C. Side B C is the base and the top vertex is A. Side A C is labeled as 15. Side A B is labeled as 12.5. Angle C A B is labeled as 77 degrees.
As you're given a triangle with 2 sides and an INCLUDED angle, all you have to do is use the formula for the 

area of this type of triangle: highlight_green%28matrix%281%2C3%2C+Area%2C+%22=%22%2C+%281%2F2%29bc+%2A+sin+A%29%29, where: b = AC, and c = AB.

That's all! Nothing else needs to be done!