Question

100 POINTS!! Find the indicated angle or side. Give an exact answer.

Find the measure of angle A in degrees.

Answer 1

A = 120°

Explanation:

We can use the cosine rule to solve for angle A, since lengths of all sides are known:

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

where a, b, and c are the sides opposites angles A, B, and C respectively.

∴ a = 2√3 , b = 6, c = 2

• Rearranging the formula to make A the subject:

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

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

⇒
`A = cos^(-1)((b^2 + c^2 -a^2)/(2(b)(c)) )`

• Now we can substitute the values into the equation to calculate the value of angle A:

`A = cos^(-1)((6^2 + 2^2 -(2√(13))^2)/(2(6)(2)) )`

⇒
`A = cos^(-1) (-(1)/(2) )`

⇒ A = 120°

Answer 2

A = 120

Explanation:

To find angle A we will need to use the law of cosines, since we know the three sides of the triangle.

a^2=b^2+c^2−2*b*c*cosA

(2 sqrt(13)) ^2 = 6^2 + 2^2 + 2 * 6 * 2 cos A

4*13 = 36 + 4 - 24 cos A

52 = 40- 24 cos A

12 = -24 cos A

-1/2 = cos A

Take the inverse cos of each side

cos^-1(-1/2) = cos^-1(cos A)

120 = Cos A or 240 = Cos A

A cannot be greater than 180 so A = 120