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Answer:
A
Step-by-step explanation:
Remark
The largest angle is going to be opposite the longest side. Use the Cosine Law to find the angle.
Equation
a^2 = b^2 + c^2 - 2*b*c * cos(A) and you are solving for A
Givens
a = 24
b = 21
c = 7
Solution
24^2 = 21^2 + 7^2 - 2*21 * 7 * cos(A)
576 = 441 + 49 - 294 * cos(A)
576 = 490 - 294 * cos(A)
I can see by looking at it that the angle is obtuse and the triangle is scalene.
576 - 490 = - 294 * cos(A)
86 = - 294 * cos(A)
86/-294 = cos(A)
- 0.2925 = cos(A)
A = cos-1(-0.2925)
A = 107 degrees
I just noticed that you did not have to go through all that. Sorry.
Answer
Just look at the givens. The side lengths are all different. The lengths all are larger than the two remaining lengths so D (not a triangle) is not correct.
No sides are equal, the the triangle is neither isosceles or equilateral. Both B and C are wrong.
The answer is A