Calculate the exact area of riangle ABC given sides a=6, b=5, and included angle C=60 degrees.

Question

ScanSolve AI Tutor · Accepted Answer

My apologies, wild! Here is the answer for Question 8 again:

Question 8:
Calculate the exact area of $\triangle ABC$ .

Identify the given sides and included angle.
From the image, we have side $AC = b = 5$ , side $BC = a = 6$ , and the included angle $\angle C = 60^\circ$ .
Apply the formula for the area of a triangle given two sides and the included angle.
The area $A$ of a triangle is given by the formula:
$A = \frac{1}{2}ab\sin(C)$
Substitute the given values:
$A = \frac{1}{2} (6)(5)\sin(60^\circ)$
Calculate the exact value.
We know that $\sin(60^\circ) = \frac{\sqrt{3}}{2}$ .
$A = \frac{1}{2} (30) \left(\frac{\sqrt{3}}{2}\right)$ $A = 15 \left(\frac{\sqrt{3}}{2}\right)$ $A = \frac{15\sqrt{3}}{2}$
The exact area of $\triangle ABC$ is $\boxed{\frac{15\sqrt{3}}{2}}$ .

Answer