In a right-angled triangle, one of the legs is 4 and the acute angle adjacent to it is 45 degrees

In a right-angled triangle, one of the legs is 4 and the acute angle adjacent to it is 45 degrees, find the area of the triangle.

Given:

ABC – right triangle,

BC – hypotenuse,

CA = 4,

angle A = 45 degrees.

Find area Savs -?

Solution:

1) Consider a right-angled triangle ABC.

We know that the sum of the degree measures of any triangle is 180 degrees. Hence:

angle B = 180 – (angle A + angle C);

angle B = 180 – (45 + 90);

angle B = 45 degrees.

Therefore, the right-angled triangle ABC is also isosceles. Then CA = CB = 4.

2) Savs = 1/2 * BC * AC;

Sav = 1/2 * 4 * 4;

Saavs = 16/2;

Sавс = 8 – the area of the triangle ABC.

Answer: 8.