One of the acute angles of a right-angled triangle is 30 degrees. The difference between the hypotenuse

| August 3, 2021 | education

One of the acute angles of a right-angled triangle is 30 degrees. The difference between the hypotenuse and the smaller leg is 15 cm. Find the hypotenuse and the smaller leg.

From the condition, we know that one of the acute angles of a right-angled triangle is 30 °, and the difference between the hypotenuse and the smaller leg is 15 cm.

It is known that a leg lying opposite an angle of 30 ° is equal to half of the hypotenuse, and it is also known that opposite the smaller angle of a right-angled triangle lies the smaller side.

Let’s compose and solve the equation.

Let the smallest leg be x and the hypotenuse be 2x.

Based on the condition:

2x – x = 15;

x = 15 cm smaller leg of a right-angled triangle.

We are looking for the hypotenuse: 2x = 2 * 15 = 30 cm.



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