Question

QUICK WHO EVER GETS THIS RIGHT WILL GET BRAINLIST In the right △ABC with m∠C=90°, m∠B=75°, and AB=12 cm. Find the area of △ABC.

Answer 1

Find AC:

Sin θ = opp/hyp

sin (75) = AC/12

AC = 12 sin(75)

Find BC:

Cos θ = adj/hyp

cos (75) = BC/12

BC = 12 cos (75)

Find Area:

Area = 1/2 x base x height

Area = 1/2 x 12 cos (75) x 2 sin(75)

Area = 18 cm²

Answer: The area is 18 cm²

Answer 2

For a 15-75-90 triangle, Altitude is equal to 1/4 of the hypotenuse, in this case, draw CE altitude from the 90 degree angle. AB= 12, AB which is the hypotenuse is 4 times larger than the altitude so that means the altitude is equal to 3.

Hence, Area of the Triangle ABC is 1/2x b x h =1/2* 12x3= 18 cm2