Question

HELP PLEASE

Given: a = 3, b = 4,
and c = 6. What is the measure of angle A to the
nearest tenth?

Answer 1

26.4

Explanation:

Law Of Cosines:

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

This should work for any side. This can generally be thought as:

`cos(\text{angle}) = \frac{\text{sum of squares of two other sides-opposite side squared}}{\text{2 times the product of the other two sides}}`

If this is too confusing here's the formula for the other sides (which is essentially the same, just different variables)

`cos(B)=(a^2+c^2-b^2)/(2ac)`

`cos(C) =(a^2+b^2-c^2)/(2ab)`

Anyways now just plug in the known values into the equation

`cos(A)=(4^2+6^2-3^2)/(2(6)(4))\\`

Square and multiply values

`cos(A)=(16+36-9)/(48)`

Add the values in the numerator

`cos(A)=(43)/(48)`

Take the inverse of cosine on both sides

`A=cos^(-1)((43)/(48))`

calculate arccosine (inverse cosine) using a calculator

`A\approx 26.384`

Round to nearest tenth

`A\approx26.4`