Question

В прямоугольном треугольнике АВС угол С равен 90 градусов, гипотенуза АВ=5 см, sinA=0,6. Найдите катет ВС. Можно, пожалуйста, с решением.

Answer 1

Вспоминаем, что
sin²α + cos²α = 1
cos²α = 1-0.36 = 0.64 
cos α = 0.8
Один катет равен 
a = АВ*sinα = 3
b = AB* cosα = 4 и получаем "египетский" треугольник Пифагора  со сторонами 3, 4 и 5.
Даже проверять не надо.

Answer 2

Solution for Finding the Length of Side BC in a Right-Angled Triangle

Given: - In a right-angled triangle ABC, angle C is 90 degrees. - The length of the hypotenuse AB is 5 cm. - sin(A) = 0.6.

Solution:

We can use the given information to find the length of side BC in the triangle.

1. Using the Sine Function: - We know that sin(A) = opposite/hypotenuse. - Therefore, sin(A) = BC/AB. - Substituting the given values, we get: 0.6 = BC/5.

2. Finding the Length of Side BC: - Rearranging the equation, we get: BC = 5 * sin(A). - Substituting the value of sin(A) = 0.6, we get: BC = 5 * 0.6. - Therefore, BC = 3 cm.

Conclusion:

The length of the side BC in the right-angled triangle ABC is 3 cm.