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Given that B = arcsin(24/25), C = arcsin(12/13), and a = 17, find the area of triangle ABC.

 

 Jul 27, 2020
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Draw altitude AP with P on BC.

 

Since B = arcsin(24/25), sides AP and AB ( of triangle(APB) ) must be in the ratio 24/25.

 

Since C = arcsin(12/13), it is also true that C = arcsin(24/26) and that sides AP and AC

( of triangle(APB) ) must be in the ratio 24/26.

 

In triangle(APB), if AP = 24 and AB = 25, then BP = 7 (Pythagorean Theorem).

In triangle(APC), if AP = 24 and AC = 26, then CP = 10.

 

Since BP + CP = BC and since 7 + 10 = 17, BP must equal 10 and CP must equal 7.

 

The area of triangle(ABC) = ½·base·height =  ½·BC·PA = ½·17·24 = .........

 Jul 28, 2020

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