The hypotenuse of a right-angled triangle is 18cm, and one of its corners is 60o. Find the area and perimeter of the triangle.

The hypotenuse of a right-angled triangle is 18cm, and one of its corners is 60o. Find the area and perimeter of the triangle.  

In a right-angled triangle ABC, we determine the value of the angle CBA. Angle CBA = 180 – 90 – 60 = 300. Then the leg AC lies opposite the angle 300 and is equal to half the length of the hypotenuse AB. AC = AB / 2 = 18/2 = 9 cm.

Determine the length of the BC leg. BC = AC * Sin600 = 18 * √3 / 2 = 9 * √3 cm.

Determine the area of the triangle.

Savs = AC * BC / 2 = 9 * 9 * √3 / 2 = 40.5 * √3 cm2.

Determine the perimeter of the triangle.

Ravs = AB + BC + AC = 18 + 9 * √3 + 9 = 27 + 9 * √3 cm.

Answer: The area of the triangle is 40.5 * √3 cm2, the perimeter of the triangle is 27 + 9 * √3 cm.




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