A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

Question

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

1 Answer

Impact of this question

1370 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-30T12:09:02

The area of the triangle is $2.5$ $2.5$ sq.unit

Explanation:

The angle between sides $A and C$ $A and C$ is $∠ b = \frac{7 π}{24} = {52.5}^{0}$ $/_b=(7pi)/24=52.5^0$
The angle between sides $B and C$ $B and C$ is $∠ a = \frac{5 π}{24} = {37.5}^{0}$ $/_a=(5pi)/24=37.5^0$
The angle between sides $A and B$ $A and B$ is $∠ c = 180 - (52.5 + 37.5) = 90^{0}$ $/_c=180-(52.5+37.5)= 90^0$
The area of the triangle with sides $A = 1, B = 5$ $A=1 , B=5$ and their included angle $∠ c = 90^{0}$ $/_c=90^0$ is $A_{t} = \frac{a \cdot b \cdot sin c}{2} = \frac{1 \cdot 5 \cdot sin 90}{2} = \frac{5}{2} = 2.5 s q . u n i t$ $A_t=(a*b*sinc)/2 = (1*5*sin90)/2=5/2=2.5 sq.unit$ [Ans]

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is 7π24(7pi)/24 and the angle between B and C is 5π24 (5pi)/24. What is the area of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?