A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is $\frac{π}{2}$ $(pi)/2$ and the angle between B and C is $\frac{π}{3}$ $(pi)/3$ . 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 5 and 8, respectively. The angle between A and C is $\frac{π}{2}$ $(pi)/2$ and the angle between B and C is $\frac{π}{3}$ $(pi)/3$ . What is the area of the triangle?

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Answer 1 · 2016-02-12T08:38:28

≈ 15.6

Explanation:

since the angle between A and C is $\frac{π}{2}$ $pi/2$
then triangle ABC is right , with hypotenuse B.

the area is therefore $\frac{1}{2} A C$ $1/2AC$

To find C , use Pythagoras' Theorem.

$C = \sqrt{8^{2} - 5^{2}} = \sqrt{64 - 25} = \sqrt{39}$ $C = sqrt( 8^2 - 5^2) = sqrt(64 - 25) = sqrt39$

hence area = $\frac{1}{2} \times 5 \times \sqrt{39} \approx 15.6$ $1/2 xx 5 xx sqrt39 ≈ 15.6$

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is $\frac{π}{2}$ $(pi)/2$ and the angle between B and C is $\frac{π}{3}$ $(pi)/3$ . 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 5 and 8, respectively. The angle between A and C is $\frac{π}{2}$ $(pi)/2$ and the angle between B and C is $\frac{π}{3}$ $(pi)/3$ . What is the area of the triangle?