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

Find the measure of angle A in degrees.

100 POINTS!! Find the indicated angle or side. Give an exact answer. Find the measure-example-1
User Giang Le
by
3.5k points

2 Answers

16 votes
16 votes

Answer:

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°

User Frank Heikens
by
2.3k points
13 votes
13 votes

Answer:

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

User Dubnde
by
2.5k points
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