Question

Решите задачи по геометрии для 8 класса. Дано: Δ ABC ∠С=90° ∠B=60° AB=10 Найти ∠A , BC. Помогите пожалуйста.(для решения нужно нарисовать треугольник)

Answer 1

Итак, во-первых найдем угол А, как мы знаем,что сумма углов треугольника равна 180 градусам, а следовательно 180- 90 -60=30- угол А
Теперь найдем сторону вс, ав- гипотенуза=10, действуем по правилу, катет лежащий против угла в 30 градусов равен половине гипотенузы, следовательно вс= 10:2=5
Удачи!

Answer 2

Problem Statement

We are given a triangle ABC, where angle C is 90 degrees, angle B is 60 degrees, and AB is 10 units long. We need to find angle A and the length of BC.

Solution

To solve this problem, we can use the trigonometric functions sine, cosine, and tangent. Let's start by finding angle A.

Since angle C is 90 degrees, triangle ABC is a right triangle. In a right triangle, the sum of the angles is always 180 degrees. Therefore, angle A can be found by subtracting angles B and C from 180 degrees:

Angle A = 180 degrees - Angle B - Angle C

Substituting the given values, we have:

Angle A = 180 degrees - 60 degrees - 90 degrees

Simplifying, we get:

Angle A = 30 degrees

Now, let's find the length of BC. We can use the trigonometric function sine to find the length of the side opposite angle A. The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the hypotenuse is AB, which is 10 units long.

sin(A) = opposite / hypotenuse

Substituting the values, we have:

sin(30 degrees) = BC / 10

To find BC, we can rearrange the equation:

BC = sin(30 degrees) * 10

Using a calculator, we can find the value of sin(30 degrees) to be approximately 0.5. Therefore:

BC = 0.5 * 10 = 5 units

So, the length of BC is 5 units.

To summarize: - Angle A is 30 degrees. - The length of BC is 5 units.

I hope this helps! Let me know if you have any further questions.