Question

In triangle ABC, AC =24, the measure of angle A = 30 degree , and the measure of angle B = 45 degree . Find the area of this triangle. (Hint: Draw a picture and include the altitude from vertex C to the side AB.)

Answer 1

Answer:

142.932

Step-by-step explanation:

given that in triangle ABC, AC =24

Angle A = 30 and Angle B =45

If we draw altitude from C, we get

h = 24sin 30 = 12

Since BC = h (45, 45,90 triangle)

BC=12

By sine formula for triangle

$\frac{12}{sin30} =\frac{AB}{sin(180-45-30)} \\AB = 24 sin 105 = 23.1822$

Area of triangle

= $1/2 (23.1822)(12)\\= 142.932$