The leg of a right-angled triangle is 21 cm, and the hypotenuse is 35 cm. Determine the height of this triangle.

Let’s first find the second leg of the right triangle. For this we will use the Pythagorean theorem.

The square of the hypotenuse is equal to the sum of the squares of the legs.

a ^ 2 + b ^ 2 = c ^ 2;

The leg of a right-angled triangle is 21 cm, and the hypotenuse is 35 cm.

x ^ 2 = 352 – 212;

x ^ 2 = 1225 – 441;

x ^ 2 = 784;

x = 28.

Let’s remember two formulas for finding the area of ​​a triangle.

The area of ​​a triangle is half the product of the legs and the area of ​​the triangle is half the product of the hypotenuse and the height drawn to the hypotenuse.

S = (a * b) / 2; S = (c * h) / 2;

(a * b) / 2 = (c * h) / 2;

a * b = c * h;

h = (a * b) / c;

h = (21 * 28) / 35 = 16.8 cm.



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