Area of a Triangle

[sam26880]

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What's the area of this triangle?

I've tried it but I got stuck. Am I right? Please check the diagram below?

I think I am doing this wrong but when you have a 30, 60, 90 triangle and if you know AB is 16 then doesn't that make the shorter leg 8 and the other leg sqrt(3) * 8? so then you would just do (1/2) * base * height and get 40*sqrt(3) but that's not the answer. The answer is 40. Can someone explain?

 

[mynamemule]

The shortest side is the opposite side of the smaller angle. So the opposite of 30 degrees would be half of the hypontenuse. The remaining side opposite of 60 degrees would be sqrt of 3.

 

[Mstoothlady2012]

if you do sin 30 = x (perpendicular line that you drew)/AB
hence x = sin 30 (AB)
= 1/2 (16)
= 8

ARea = 1/2 (8)(10)
= 40

the perpendicular line will be 8 not the base