Question

In triangle ABC, AB = 12 inches, AC = 18 inches and the area of the triangle is 107.737 square inches. What is the measure of angle A?
A) 1.5°
B) 43°
C) 86°
D) 172°

Answer 1

Your answer is c, 86 degrees. Use the sine function, which is depicted in the image below. Hope this helped.

Answer 2

Answer:

(C)$86^{\circ}$

Step-by-step explanation:

It is given that In triangle ABC, AB = 12 inches, AC = 18 inches and the area of the triangle is 107.737 square inches.

Now, using the formula $Area=\frac{absinC}{2}$ where a and b are the two sides of the triangle and the C is the included angle, therefore

We have AB=12 in and AC=18 in and area= 107.737 square inches.

Substituting these values in the above equation, we get

$107.737=\frac{12{\times}18sinA}{2}$

$107.737=108sinA$

$\frac{107.737}{108}=sinA$

$0.997=sinA$

$A=sin^{-1}(0.997)$

$A=85.56^{\circ}$

$A$≈$86^{\circ}$

Thus, option (C) is correct.