Question

How do you solve the triangle given `w=20, x=13, y=12`?

Answer 1

"W," "X," and "Y," refer to the angles opposite sides "w," "x," and "y."

`W = 106.1913516^o`
`X = 38.62483288^o`
`Y = 35.18381552^o`

Explanation:

"W," "X," and "Y," refer to the angles opposite sides "w," "x," and "y."

Start by finding any angle using the Law of Cosines.
`cos(A)=(b^2+c^2-a^2)/(2bc)`
Plugging in the numbers, we get:
`cos(W)=(13^2+12^2-20^2)/(2*13*12)`
Therefore,
`cos^(-1)((13^2+12^2-20^2)/(2*13*12))=W`
Simplifying inside of the parentheses, we get:
`cos^(-1)((-29)/104)=W`
Therefore, the measure of angle W is about
`106.1913516^o`

Next, we can apply the Law of Sines.
`sin(106.1913516^o)/20=sin(X)/13`
Rearranging the numbers, we get:
`13sin(106.1913516^o)/20=sin(X)`
Therefore,
`X=sin^(-1)(13sin(106.1913516^o)/20)`
Therefore, the measure of angle X is about
`38.62483288^o`

Lastly, we can apply the truth that the sum of all interior angles in a triangle is `180^o`.
`180^o - 106.1913516^o - 38.62483288^o = Y`
Simplifying, we find the measure of angle Y to be about:
`35.18381552^o`

Therefore, the measure of angle W is `106.1913516^o`, the measure of angle X is `38.62483288^o`, and the measure of angle Y is `35.18381552^o`.