A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2 and the angle between sides B and C is pi/12. If side B has a length of 4, what is the area of the triangle?

1 Answer
turksvids
Jan 4, 2018

8tan(pi/12) = 16-8sqrt(3) approx 2.146

Explanation:

From the given we know that:

Angle C has measure pi/2 (so we have a right triangle).
Angle A has measure pi/12.

We know that side b has length 4.

It's helpful to draw a right triangle with hypotenuse c, right angle C, and the rest of the given information filled in.

Since side b is adjacent to angle A we can use tangent to find side a.

tan(A) = a/b

tan(pi/12) = a/4\rightarrow a = 4tan(pi/12).

Since a and b are the legs of the right triangle the area of the triangle is 1/2a*b so the area is 1/2*(4tan(pi/12)*4) =8tan(pi/12) = 16-8sqrt(3) approx 2.146.

I used a calculator for the to numerical values.

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