Question

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

URGENT! PLEASE HELP SOLVE BEFORE 9:30 a.m. FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! THANK YOU SO MUCH!

Answer 1

Given : m∠A = 60°, m∠C = 45°.

We know that Sum of interior angles of a triangle = 180°.

⇒ m∠A + m∠B + m∠C = 180

⇒ 60 + m∠B + 45 = 180

⇒ 105 + m∠B = 180

⇒ m∠B = 180 - 105

⇒ m∠B = 75°.

Now,

Given, AB = 8. We have to calculate BC and AC:

We have to use the Law of cosines in order to find an unknown angle:

⇒ (a/sinA) = (b/sinB) = (c/sinC)

(i)

⇒ (AB/sinC) = (BC/sinA)

⇒ (8/sin 45°) = (BC/sin 60°)

⇒ (8/0.707) = (BC/0.866)

⇒ 6.928 = 0.707 BC

⇒ BC = 9.799

(ii)

⇒ (AB/sin C) = (AC/sin B)

⇒ (8/sin 45°) = (AC/sin 75°)

⇒ AC = 10.928.

Perimeter of ΔABC

⇒ AB + BC + AC

⇒ 8 + 10.928 + 9.799

⇒ 28.728

Area of ΔABC:

⇒ (1/2) * AB * AC * sin(60)

⇒ (1/2) * 8 * 10.928 * (√3/2)

⇒ 2 * 10.928 * 1.732

⇒ 37.85

Hope it helps!