Question

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 67°, a = 10 cm, c = 20 cm 92.05 cm2 184.1 cm2 100 cm2 39.07 cm2

Answer 1

Among many other formulas, the area of a triangle is

$S = \frac 1 2 a c \sin B$

where B is the angle between sides a and c.

$S=\frac 1 2(10)(20) \sin 67^\circ \approx 92.05 \textrm{ sq cm}$

Answer: 92.05 sq cm, first choice

Bonus. Here's a formula for the area S of a triangle your teacher doesn't know:

$16S^2 = 4a^2b^2 -(c^2-a^2-b^2)^2=(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)$