A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/3, the angle between sides B and C is pi/6, and the length of B is 15, what is the area of the triangle?

2 Answers
Dec 23, 2017

this is a 30-60-90 angle triangle .
length of hypoteneuse is given that is B=15
using trignometry
A=B×sin30° C=B×cos30°
Area of triangle ABC =A×C×1/2
=1/2×B×sin30°×B×cos30°
=1/2×B^2×1/2×sqrt3/2
=1/2×15^2×sqrt3/4
=1/2×225×sqrt3/8
~~48.7139289629

Dec 23, 2017

225sqrt(3)/8

Explanation:

We know that pi/6 "radians"=30^o and pi/6 "radians"=60^o, so we are dealing with a 30-60-90 triangle.

If side B touches both the 30-degree angle and the 60-degree angle, then side B is opposite the 90-degree angle and is the hypotenuse of the triangle.

Since we know that the sides of a 30-60-90 triangle follow the pattern x-xsqrt(3)-2x, we can say that:

2x=15

x=15/2

xsqrt(3)=15/2*sqrt(3)

Now that we know the base and height of the triangle, we can find the area.

"Area" = 1/2*(x)*(xsqrt(3))

=1/2*15/2*15/2*sqrt(3)

=225sqrt(3)/8