A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 20, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 20, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?

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Answer 1 · 2015-12-16T03:36:29

22.96 (approx) sq units

Explanation:

Sides are marked with small letters. So the sides are a,b,c. Triangle is ABC. Side opposite A is a, side opposite B is b...... The triangle is like this enter image source here

The area of the triangle would be $\frac{1}{2} a b sin C$ $1/2 ab sinC$

= $\frac{1}{2} 120 sin (\frac{π}{8})$ $1/2 120 sin (pi/8)$ = 60(0.3826)=22.96 (approx).

For exact value write $cos (\frac{π}{4}) = 1 - 2 {sin}^{2} (\frac{π}{8})$ $cos(pi/4)= 1-2sin^2 (pi/8)$ , that is

$\frac{1}{\sqrt{2}} = 1 - 2 {sin}^{2} (\frac{π}{8})$ $1/sqrt2 =1-2sin^2 (pi/8)$ . Simplify for $sin (\frac{π}{8})$ $sin(pi/8)$ and plug in the Area expression $60 sin (\frac{π}{8})$ $60 sin (pi/8)$

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 20, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 20, respectively. The angle between A and C is 17π24(17pi)/24 and the angle between B and C is π8 (pi)/8. What is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 20, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?