# In a right-angled triangle ABC, the hypotenuse AB is 13 cm. Find the leg BC if tg B = 2.4

March 28, 2021 | education

| 1. Given that the tangent is the ratio of the opposite leg to the adjacent leg, we find

the ratio of the opposite AC leg to the adjacent BC leg:

AC / BC = 2.4;

2. For convenience of further calculations, takes the length of the BC leg as x, the AC leg length

2.4x.

3. Using the Pythagorean theorem, we compose the equation:

13 ^ 2 = x ^ 2 + (2.4x) ^ 2;

169 = x ^ 2 + 5.76 x ^ 2 = 6.76 x ^ 2;

x ^ 2 = 169 / 6.76 = 25;

x = 25 centimeters.

Answer: the length of the BC leg is 25 centimeters.

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