In triangle ABC, angle C = 90 °, angle A = 45 °, AC = 3 AB = 8. Find S of the triangle.

Given:
right-angled triangle ABC,
angle C = 90 °,
angle A = 45 °,
AC = 3,
AB = 8.
Find S of triangle ABC-?
Solution:
Consider a right-angled triangle ABC. We know that the sum of the degree measures of any triangle is 180 degrees. Consequently:
angle B = 180 – (angle A + angle C);
angle B = 180 – (45 + 90);
angle B = 180 – 135;
angle B = 45 degrees;
Then triangle ABC is isosceles. So AC = CB = 3.
S triangle ABC = 1/2 * AC * BC;
S triangle ABC = 1/2 * 3 * 3;
S triangle ABC = 9/2;
S triangle ABC = 4.5.
Answer: 4.5.