Question

В треугольнике АВС угол С равен 90 , АС=3 , tgВ=0,3. Найдите площадь АВС . Помогите пожалуйста

Answer 1

Ответ:

Объяснение:

tgВ=АС/ВС=0,3

3/ВС=0,3

ВС=3÷0,3

ВС=10 см

S= 1/2×AC×BC=1/2×3×10=15 см²

Answer 2

Problem Analysis

We are given a triangle ABC with angle C equal to 90 degrees, AC equal to 3, and tg(B) equal to 0.3. We need to find the area of triangle ABC.

Solution

To find the area of triangle ABC, we can use the formula: Area = (1/2) * base * height.

First, let's find the base and height of the triangle.

Since angle C is 90 degrees, triangle ABC is a right-angled triangle. The side AC is the base, and the side BC is the height.

Given that AC = 3, we can use the Pythagorean theorem to find BC. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have: BC^2 = AC^2 - AB^2

Since AB is the height of the triangle, we can rewrite the equation as: BC^2 = AC^2 - height^2

Substituting the given values, we have: BC^2 = 3^2 - height^2

Since tg(B) = 0.3, we can use the definition of tangent to find the height: tg(B) = height / AC 0.3 = height / 3 height = 0.3 * 3 height = 0.9

Substituting the value of the height back into the equation for BC^2, we have: BC^2 = 3^2 - 0.9^2 BC^2 = 9 - 0.81 BC^2 = 8.19 BC ≈ √8.19 BC ≈ 2.86

Now that we have the base (AC = 3) and the height (BC ≈ 2.86), we can calculate the area of triangle ABC: Area = (1/2) * base * height Area = (1/2) * 3 * 2.86 Area ≈ 4.29 square units.

Therefore, the approximate area of triangle ABC is 4.29 square units.

Conclusion

The approximate area of triangle ABC is 4.29 square units.