A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{π}{2}$ $(pi)/2$ , and the length of B is 12, what is the area of the triangle?

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{π}{2}$ $(pi)/2$ , and the length of B is 12, what is the area of the triangle?

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Answer 1 · 2016-02-26T22:15:15

$A = 72 (1 + \sqrt{2})$ $A = 72(1+sqrt2)$

Explanation:

Lets take a look at the triangle.

Geogebra

The area of a triangle is given by the formula;

$A = \frac{1}{2} base \times height$ $A = 1/2 "base" xx "height"$

The angle $\frac{π}{2}$ $pi/2$ is a right angle, so the area of our triangle is;

$A = \frac{1}{2} B \times C$ $A= 1/2 B xx C$

We are given the length of $B$ $B$ , and we can solve for $C$ $C$ using the tangent formula.

$tan θ = \frac{C}{B}$ $tan theta = C/B$

$tan (\frac{3 π}{8}) = \frac{C}{12}$ $tan ((3pi)/8) = C/12$

$C = 12 tan (\frac{3 π}{8})$ $C = 12 tan ((3pi)/8)$

We can solve for $tan (\frac{3 π}{8})$ $tan((3pi)/8)$ using a calculator or using the half angle formula. Since its not the emphasis of the problem, I'll just include a link to the solution here. The punch line is;

$tan (\frac{3 π}{8}) = 1 + \sqrt{2}$ $tan((3pi)/8) = 1+ sqrt(2)$

So our area function becomes;

$A = \frac{1}{2} B \times C = \frac{1}{2} (12) (12 (1 + \sqrt{2}))$ $A = 1/2 BxxC = 1/2(12)(12(1+sqrt2))$

$A = 72 (1 + \sqrt{2})$ $A = 72(1+sqrt2)$

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{π}{2}$ $(pi)/2$ , and the length of B is 12, what is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. If the angle between sides A and B is 3π8(3pi)/8, the angle between sides B and C is π2(pi)/2, and the length of B is 12, what is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{π}{2}$ $(pi)/2$ , and the length of B is 12, what is the area of the triangle?