In triangle ABC, angle A is 51 (0 at the top). Find the angle C. 2) In a triangle, ABC, AD is the height

In triangle ABC, angle A is 51 (0 at the top). Find the angle C. 2) In a triangle, ABC, AD is the height, the angle BAD is. Find corner C.

1) Since the sum of the angles of the triangle is 180 degrees, we get:

∠C + ∠B + ∠A = 180;

∠C = 180 – 51 – ∠B = 129 – ∠B.

2) Find the side AB:

AB = h / cos (BAD), where h is the height.

The angle ABC is equal to:

ABC = 90 – BAD.

By the sine theorem, we get the expression:

AB / sin (C) = AC / sin (ABC).

Since AC = h / sin (C), the expression becomes:

h / cos (BAD) * sin (C) = h sin (C) / sin (ABC).

Reduce by h, we get:

sin ^ 2 (C) = sin (ABC) / cos (BAD);

C = arcsin (√sin (ABC) / cos (BAD)).