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°

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Mathunga Mathunga · Answer 1 · 2018-05-21T01:19:41+02:00

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

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boffeemadrid boffeemadrid · Answer 2 · 2019-05-30T11:37:29+02:00

Answer:

(C)[tex]86^{\circ}[/tex]

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 [tex]Area=\frac{absinC}{2}[/tex] 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

[tex]107.737=\frac{12{\times}18sinA}{2}[/tex]

[tex]107.737=108sinA[/tex]

[tex]\frac{107.737}{108}=sinA[/tex]

[tex]0.997=sinA[/tex]

[tex]A=sin^{-1}(0.997)[/tex]

[tex]A=85.56^{\circ}[/tex]

[tex]A[/tex]≈[tex]86^{\circ}[/tex]

Thus, option (C) is correct.