Question

How do you solve the triangle given ∠A = 73°, a = 18, b = 11?

Answer 1

`/_A ~= 71˚`

`/_B ~= 36˚`

`C ~= 17.80`

Explanation:

Start by drawing a diagram.

As you can see, we know the measure of an angle and a side that are opposite. This triangle can therefore be solved using The Law of Sines.

`sinA/a = sinB/b`

`(sin 73˚)/18 = sinB/11`

`B ~= 36˚`

Beware that although the situation (knowing two sides and an angle opposite one of the sides) is the "ambiguous case", this triangle has only one solution. This is because if it had two solutions, the second angle `B` would be `180˚ - 36˚ = 144˚`, and when angle B is `144˚`, the sum of `73˚` and `144˚` exceeds `180˚`, which is more than the sum of the angles in a triangle can be.

`A = 180˚ - 36˚ - 73˚ ~= 71˚`

The last step in this problems is to determine the length of side C. This can be done by using The Law of Sines.

`(sin71˚)/C = (sin73˚)/18`

`C ~= 17.80`

In summary:

`/_A ~= 71˚`

`/_B ~= 36˚`

`C ~= 17.80`

Hopefully this helps!