Question

Which of the following choices

is the area of triangle ABC
rounded to the nearest square
mile?

353 square miles
516 square miles
611 square miles
674 square miles

Answer 1

Denote AH as height of triangle ABC, with H lies on BC.

Applying sine theorem:

AH/AC = sin 60

=> AH = AC x sin 60 = 47 x sqrt(3)/2 = 40.7

=> Area of triangle ABC is calculated by:

A = AH x BC x (1/2) = 40.7 x 30 x (1/2) = 610.5 = ~611

=> Option C is correct.

Hope this helps!

:)