Question

Find the measure of angle A using the Law of Cosines. Picture is not drawn to scale A= Round at least one decimal place .

Answer 1

The Law of Cosines tells us that, given any triangle ABC:

Then:

`a^2=b^2+c^2-2bc\cos(A)`

In this case:

a = 21

b = 23

c = 17

By the Law of Cosines:

`21^2=23^2+17^2-2\cdot23\cdot17\cdot\cos(A)`

And solve:

`\begin{gathered} 441=529+289-782\cos(A) \\ . \\ 441-818=-782\cos(A) \\ . \\ (-377)/(-782)=\cos(A) \end{gathered}`

Now we can apply arc cosine on both sides:

`A=\cos^(-1)((377)/(782))\approx61.1775`

The answer is, to one accurate decimal place:

A = 61.18 degrees.