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 13, what is the area of the triangle?
1 Answer
Explanation:
Our goal will be to use
Step 1: Find the value of
Using the fact that the sum of all 3 angles in a triangle is
pi , we get
angle A + angle B + angle C = pi
pi/6" "+ angle B + pi / 3" "= pi
" "angle B " "= pi/2 So
angle B = pi/2 .
Step 2: Find the length of
We now use the sine law for triangles to get
a/sinA=b/sinB
a/sin(pi/6)=13/sin(pi/2)
" "a" "=(13sin(pi/6))/sin(pi/2)
" "a" "=(13(1/2))/(1)=13/2 So
a=13/2 .
Step 3: Find the area of the triangle.
We can now use the following formula for a triangle's area:
A_triangle=1/2 a b sin C
A_triangle=1/2 * 13/2 * 13 * sin (pi/3)
A_triangle=169/4 * sqrt 3 / 2
A_triangle=(169sqrt 3)/8" "approx 36.59 .