Question

Find all solutions for a triangle with A=140, b=10, and a=3 a. B = 15.4°; C = 147.6°; c = 20.2 c. B = 15.4°; C = 134.5°; c = 20.2 b. B = 16.2°; C = 147.6°; c =20.2 d. no solutions

Answer 1

do you know that the biggest angle goes with the biggest side. if angle A is 140 degrees) then the other two angles *together* add up to 40 degrees) so both B and C are less than 40. that means their sides are less than the side opposite angle A, so less than 3. But they tell you b is 10. that is not possible.

Answer 2

Option D. No solutions.

Explanation:

We know in a triangle, sum of all angles is equal to 180°

Therefore, ∠A + ∠B + ∠C = 180°

Angle A is given as 140°

Now we go through the measure of angles given in each option.

A). ∠A + ∠B + ∠C = 180°

140 + 15.4 + 147.6 = 303°

Which is not possible in a triangle. Incorrect option.

B). 140 + 16.2 + 147.6 = 303.8

But for a triangle sum of angles should be 180° so this triangle is not possible. Incorrect option.

C). 140 + 15.4 + 134.5 = 279.9°

Again not possible. Incorrect option.

D). No solutions is the correct option.