Question

100 POINTS!! Find the indicated angle or side. Give an exact answer.
Find the measure of angle A in degrees.

Answer 1

Answer:

A = 120

Step-by-step 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

Answer 2

Answer:

A = 120°

Step-by-step 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:

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

⇒  $cos A = \frac{b^2 + c^2 -a^2}{2(b)(c)}$

⇒  $A = cos^{-1}(\frac{b^2 + c^2 -a^2}{2(b)(c)} )$

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

$A = cos^{-1}(\frac{6^2 + 2^2 -(2\sqrt{13})^2}{2(6)(2)} )$

⇒  $A = cos^{-1} (-\frac{1}{2} )$

⇒  A = 120°