Find the area of a right-angled triangle if its hypotenuse is 16 cm and one of the angles of the triangle is 45 degrees.

Since triangle ABC is rectangular, and one of its acute angles is 450, the second angle is: (180 – 90 – 45) = 450, and therefore, triangle ABC is rectangular isosceles, AB = BC.

Let us determine the length of the leg AC through the cosine of the included angle.

AC = BC * CosACB = 16 * Cos45 = 16 * √2 / 2 = 8 * √2 cm.

AC = AB = 8 * √2 cm.

Determine the area of the triangle.

Savsd = AB * AC / 2 = 8 * √2 * 8 * √2 / 2 = 64 cm2.

Answer: The area of the triangle is 64 cm2.