Question

Дано прямоугольный треугольник АВС АВ=8см угол А=30градусов найти АС и ВС и площадь Треугольника АВС

Answer 1

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Answer 2

Given Information:

We are given a right triangle ABC, where AB = 8 cm and angle A = 30 degrees. We need to find the lengths of AC and BC, as well as the area of triangle ABC.

Solution:

To find the lengths of AC and BC, we can use trigonometric ratios. Since angle A is 30 degrees and AB is the side opposite angle A, we can use the sine function to find AC:

AC = AB / sin(A)

Similarly, we can use the cosine function to find BC:

BC = AB / cos(A)

To find the area of triangle ABC, we can use the formula:

Area = (1/2) * AB * BC

Let's calculate the values step by step:

1. Calculate AC: - Using the sine function: AC = AB / sin(A) - Substituting the given values: AC = 8 cm / sin(30 degrees) - Evaluating the expression: AC ≈ 16 cm.

2. Calculate BC: - Using the cosine function: BC = AB / cos(A) - Substituting the given values: BC = 8 cm / cos(30 degrees) - Evaluating the expression: BC ≈ 9.24 cm.

3. Calculate the area of triangle ABC: - Using the formula: Area = (1/2) * AB * BC - Substituting the given values: Area = (1/2) * 8 cm * 9.24 cm - Evaluating the expression: Area ≈ 37 cm².

Summary:

- The length of AC is approximately 16 cm. - The length of BC is approximately 9.24 cm. - The area of triangle ABC is approximately 37 cm².