A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{6}$ $pi/6$ . If side B has a length of 7, what is the area of the triangle?

Question

1562 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-25T08:24:43

Angle C= $\frac{5 π}{12}$ $(5pi)/12$ given, angle A= $\frac{π}{6} [= \frac{2 π}{12}]$ $pi/6[=(2pi)/12]$ also given

so angle B = $\frac{12 π - 7 π}{12} = \frac{5 π}{12}$ $[12pi-7pi]/12=(5pi)/12$

This means the triangle is isosceles and side c will be length 7.

Area is $\frac{1}{2}$ $1/2$ absinC

Area= $\frac{1}{2} \times 7 \times 7 \times sin [\frac{π}{6}]$ $1/2xx7xx7xx sin[[pi]/6]$

Area = $\frac{1}{2} \times 49 \times \frac{1}{2}$ $1/2xx49xx1/2$

Area= $\frac{49}{4}$ $49/4$

Area = $12 \frac{1}{4} u n i t s^{2}$ $12 1/4 units^2$

A triangle has sides A, B, and C. The angle between sides A and B is 5π12(5pi)/12 and the angle between sides B and C is π6pi/6. If side B has a length of 7, what is the area of the triangle?