In a right-angled triangle, the hypotenuse is 10 and one of the acute angles is 30 degrees. Find the area of a triangle divided by √3.

First way.

In a right-angled triangle ABC, Cos30 = AC / AB.

AC = AB * Cos30 = 10 * √3 / 2 = 5 * √3 cm.

Then Savs = AC * AB * Sin30 / 2 = (5 * √3) * 10 * (1/2) / 2 = 50 * √3 / 4 = 12.5 * √3 cm2.

Savs / √3 = 12.5 cm2.

Second way.

The CB leg lies opposite an angle of 30, then CB = AB / 2 = 10/2 = 5 cm.

Then AC ^ 2 = AB ^ 2 – CB ^ 2 = 100 – 25 = 75.

AC = 5 * √3 cm.

Savs = AC * BC / 2 = 5 * √3 * 5/2 = 12.5 * √3 cm2.

Savs / √3 = 12.5 cm2.

Answer: 12.5 cm2.