Question

В прямоугольном треугольнике ABC гипотенуза AB равна 13 см. Найдите катет BC, если тангенс B=2.4. Ответ запишите в сантиметрах

Answer 1

TgB=AC/BC=2.4  Отсюда АС=2,4*ВС
по теореме пифагора BA^2=AС^2+BC^2= (2,4*ВС)^2+BC^2=13^2
Отсюда 6,76*ВС^2=169,    BC=5

Answer 2

Problem Analysis

We are given a right triangle ABC, where the hypotenuse AB is 13 cm. We need to find the length of the leg BC, given that the tangent of angle B is 2.4.

Solution

To find the length of BC, we can use the tangent function. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the tangent of angle B is given as 2.4, which means:

tan(B) = BC / AB

We know that AB is 13 cm, so we can substitute the values into the equation:

2.4 = BC / 13

To solve for BC, we can multiply both sides of the equation by 13:

2.4 * 13 = BC

Calculating the value:

BC ≈ 31.2 cm

Therefore, the length of the leg BC is approximately 31.2 cm.

Answer

The length of the leg BC is approximately 31.2 cm.