A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3# and the angle between sides B and C is #pi/6#. If side B has a length of 26, what is the area of the triangle?

Question

A triangle has sides A, B, and C.  The angle between sides A and B is #(pi)/3# and the angle between sides B and C is #pi/6#.  If side B has a length of 26, what is the area of the triangle?

HIX Tutor · Accepted Answer

undefined To find the area of the triangle:
1. First, calculate the height of the triangle using side B and the angle between sides B and C: height = B * sin(angle between B and C)
2. Then, find the base of the triangle using the height, side B, and the angle between sides A and B: base = height / tan(angle between A and B)
3. Finally, calculate the area of the triangle using the base and height: area = (1/2) * base * height.

Aaliyah Abdullah · Answer

#(169sqrt3)/2# The third angle #pi/2#, which means it is a right angled triangle. The three sides are #1:sqrt3:2# in length with side B being the longest. Side A is vertical to side C. Side A=#13#, side C=#13sqrt3# Area of triangle=#1/2*13*13sqrt3=(169sqrt3)/2#