In triangle ABC, m<A = 90, m<B=75, and BC = \sqrt{3}. What is the area of ABC? Express your answer as a common fraction.

Question

HELP THIS IS SO HARD HHELP MEE!!! EXplain too please!

Answer 1

You have a right-angled triangle so we can use the formula
(1/2) base x height

Since you want the answer as a common fraction, I will assume that you need "exact" values.

you state that BC = \sqrt{3}
I will assume that is meant to say √3
so cos75 =base/√3
base = √3cos75
and sin75 = height/√3
height = √3sin75

area = (1/2)(√3sin75)(√3cos75)
= (3/2)sin75cos75)
(recall sin 2A = 2sinAcosA)
= (3/2)(2sin75cos75)/2
= (3/4) sin 150

sin 150 = sin30 ---- one of the basic identities

area = (1/3) sin150
= (3/4)sin30
= (3/4)(1/2) = 3/8

Answer 2

thanks alot

Answer 3

THANK YOU !!!!!!!

Answer 4

You don't even need trig for this. Reflect B, draw and altitude from B to B'C and solve