Question

у прямокутному трикутнику АВС (кут С = 90) АС = 12 см tgB=4/3 знайдіть другий катет і гіпотенузу трикутника

Answer 1

Ответ:
СВ=9см
АВ=15см

Решение:
tgB=AC/CB
4/3=12/CB
CB=12*3/4=9см
Теорема Пифагора
АВ=√(СВ²+СА²)=√(9²+12²)=√(81+144)=
=√225=15см

Answer 2

Given Information:

We are given a right triangle ABC, where angle C is 90 degrees. We are also given that AC = 12 cm and tgB = 4/3.

Finding the Second Leg and Hypotenuse:

To find the second leg and hypotenuse of the triangle, we can use the trigonometric ratios of a right triangle.

The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, tgB = BC/AC.

Let's denote the length of the second leg as BC and the length of the hypotenuse as AB.

Using the given information, we have tgB = BC/AC = 4/3.

To find BC, we can rearrange the equation as BC = tgB * AC.

Substituting the given values, we have BC = (4/3) * 12 = 16 cm.

Therefore, the length of the second leg BC is 16 cm.

To find the length of the hypotenuse AB, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, AB^2 = AC^2 + BC^2.

Substituting the given values, we have AB^2 = 12^2 + 16^2 = 144 + 256 = 400.

Taking the square root of both sides, we have AB = √400 = 20 cm.

Therefore, the length of the hypotenuse AB is 20 cm.

Summary:

In the given right triangle ABC, where angle C is 90 degrees, AC = 12 cm, and tgB = 4/3, we have found that the length of the second leg BC is 16 cm and the length of the hypotenuse AB is 20 cm.