A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . 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 1 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . What is the area of the triangle?

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Answer 1 · 2016-04-15T07:37:06

Area of triangle is $1.449$ $1.449$ units.

Explanation:

The formula for area of a triangle given two sides $a$ $a$ and $b$ $b$ and included angle $θ$ $theta$ is $\frac{1}{2} \times a b \times sin θ$ $1/2xxabxxsintheta$ .

Here, though we have been given two sides as $1$ $1$ and $3$ $3$ , included angle has not been given.

But as other two angles are $\frac{13 π}{24}$ $(13pi)/24$ and $\frac{π}{24}$ $pi/24$ , third angle will be given by

$π - \frac{13 π}{24} - \frac{π}{24} = \frac{24 π - 13 π - π}{24} = \frac{10 π}{24}$ $pi-(13pi)/24-pi/24=(24pi-13pi-pi)/24=(10pi)/24$

Hence area of triangle is $\frac{1}{2} \times 1 \times 3 \times sin (\frac{10 π}{24})$ $1/2xx1xx3xxsin((10pi)/24)$

= $\frac{3}{2} \times 0.9659 = 1.449$ $3/2xx0.9659=1.449$ units.

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A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . What is the area of the triangle?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is 13π24(13pi)/24 and the angle between B and C is π24 (pi)/24. What is the area of the triangle?

1 Answer

Explanation:

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Impact of this question

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is $\frac{13 π}{24}$ $(13pi)/24$ and the angle between B and C is $\frac{π}{24}$ $(pi)/24$ . What is the area of the triangle?