Question

Use the Law of Sines to find mZE.

Round to the nearest degree.
D
30 mi
18 mi
78°
F
E

Answer 1

Explanation:

recall law of Sines : Sin(A) / a = Sin(B) / b

where F can be A, in above equation, and then a = 30

we want to find E so that can be B, and b = 18

Sin(78) / 30 = Sin(B) / 18

solve the parts you can

0.03260 = Sin(B) / 18

18 * 0.03260 = Sin(B)

0.5868885 = Sin(B)

use arcSin() to find angle of B

arcSin(0.586885) = arcSin( Sin(B)) [ b/c arcSin is the inverse of Sin those go away, they cancel each other out ]

35.9365 = B

36° = B ( and B = E in the given triangle )

∠E = 36°