Question

Use the figure shown to find the missing lengths of the triangle.

BC=15 ​in; find AC and AB.
(Round to the nearest thousandths)

show your work.

Answer 1

can use right angle angle trigonometry as this is a right triangle

sine is opposite over hypotenuse

sin 60 = BC/AB because opposite to 60 is BC and the hypotenuse is AB.

rearrange for AB

sin 60 = BC/AB
AB sin 60 = BC
AB = BC / sin 60

we are given that BC = 15 in

AB = 15 / sin60
AB = 17.321 in (calculator

can use tangent of 60 degrees to find AC
tangent is opposite over adjacent so

tan(60) = BC / AC
AC tan 60 = BC
AC = BC / tan 60
AC = 15 / tan 60
AC = 8.660 in