In a right-angled triangle, one of the legs is 12, and the opposite angle is 45. Find the area of the triangle.

In a right triangle it is known:

ABC – right triangle;
BC leg = 12;
Angle A = 45 °.
Find the area of the triangle.

1) The area of a right-angled triangle is half the product of their legs.

One leg BC is known, we find the second leg AC of triangle ABC.

2) Since, in the triangle ABC, 2 angles are known, 90 ° and 45 °, that is, the third angle of the triangle ABC is also 45 °.

Angle A = Angle B = 45 °.

3) Find the AC leg.

tg A = BC / AC;

AC = BC / tg A = 12 / tg 45 ° = 12/1 = 12;

4) Find the area.

S = 1/2 * BC * AC = 1/2 * 12 * 12 = 6 * 12 = 6 * 10 + 6 * 2 = 60 + 12 = 72.

Answer: S = 72.