Question

Please help

Find the value of x.
Round to the nearest tenth.
a 28
b x
22
11
x =?
c

Answer 1

69.9° or 110.1°

Explanation:

You want to know the angle opposite the side of length 22 in a triangle in which a 28° angle is opposite a side of length 11.

Law of Sines

The law of sines tells you ...

sin(B)/b = sin(A)/a

sin(x)/22 = sin(28°)/11

sin(x) = 22/11 · sin(28°)

x = arcsin(2·sin(28°)) ≈ 69.9° or 110.1°

__

Additional comment

There are generally two solutions to a Law of Sines problem in which the given angle is opposite the shorter of two given sides. The exception is when the triangle is a right triangle.