Find the unknown sides and angles of the triangle ABC, if AB = 7root2 cm, AC = 7cm, angle B = 45 degrees

Consider a triangle ABC.

By the condition of the problem, we have that

AB = 7 * √2, AC = 7, B = 45 °.

By the sine theorem, we have:

AC / sin (B) = AB / sin (C),

7 / sin (45 °) = 7 * √2 / sin (C),

sin (C) = (7 * √2 * √2 / 2) / 7 = 1,

C = 90 °.

Therefore, A = 180 ° – B – C = 180 ° – 45 ° – 90 ° = 45 °.

Since we got A = B = 45 °, then triangle ABC is isosceles and AC = BC = 7.

Therefore, triangle ABC is right-angled and isosceles. Its sides are equal:

AB = 7 * √2, AC = BC = 7, and the angles are:

A = B = 45 °, C = 90 °.