Use the sine function to find the indicated part of triangle ABC. Round to four significant digits. Find c if b = 16.48 ft and A = 38.1°.
A)26.71 ft
B)10.17 ft
C)20.94 ft
D)12.97 ft

Question

Use the sine function to find the indicated part of triangle ABC. Round to four significant digits. Find c if b = 16.48 ft and A = 38.1°. 
A)26.71 ft 
B)10.17 ft 
C)20.94 ft 
D)12.97 ft

Quizplus · Accepted Answer

Using the sine function:
sin(A) = opposite/hypotenuse
sin(38.1°) = opposite/16.48 ft
opposite = 16.48 ft * sin(38.1°)
opposite = 10.94 ft

Now, using the sine function again:
sin(C) = opposite/hypotenuse
sin(C) = 10.94 ft/c
c = 10.94 ft / sin(C)

To find C, we need to use inverse sine:
sin inverse (10.94 ft / c) = C
sin inverse (10.94 ft / 16.48 ft) = C
C = 44.34°

Now we can use the sine function one more time to find c:
sin(C) = opposite/hypotenuse
sin(44.34°) = 10.94 ft/c
c = 10.94 ft / sin(44.34°)
c ≈ 20.94 ft

Therefore, the best choice is C, which is 20.94 ft.

Use the Sine Function to Find the Indicated Part of Triangle