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°
A) 1.5°
B) 43°
C) 86°
D) 172°
Asked by: USER3733
194 Viewed
194 Answers
Answer (194)
Your answer is c, 86 degrees. Use the sine function, which is depicted in the image below. Hope this helped.
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.