Question

Найдите площадь треугольника ABC, если: ВС=3 см, АВ = = 18√2 см, ∠B=45° . Если что,то можно оочень подробно!

Answer 1

Опускаем высоту СД из С к основанию ВА. В треугольнике СВД СВ=3, угол В = 45. Из определения синуса СД/СВ = sin45, отсюда следует СД=3*sin45= 3/корень из 2.

Площадь АВС = (СД*АВ) / 2 = 3*18/2 = 27

Answer 2

Finding the Area of Triangle ABC

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

Area = (1/2) * base * height

In this case, we have the base AB and the height BC. The given information is: - BC = 3 cm - AB = 18√2 cm - ∠B = 45°

First, we need to find the length of the height BC. Then we can use the formula to calculate the area.

Calculating the Height BC

To find the length of BC, we can use trigonometric functions. Since ∠B = 45°, we can use the fact that in a right-angled triangle, the sides are related by the trigonometric functions.

Using the given information, we can use the trigonometric function to find the length of BC.

Trigonometric Calculation

We know that: - AB = 18√2 cm - ∠B = 45° - BC = 3 cm

We can use the trigonometric function tan to find the length of BC: tan(45°) = BC / AB

Calculation

tan(45°) = BC / 18√2

Solving for BC: BC = 18√2 * tan(45°)

Area Calculation

Now that we have the length of BC, we can use the formula to calculate the area of triangle ABC: Area = (1/2) * AB * BC

Substitute the values of AB and BC into the formula to find the area.

Let's calculate the area using the given values and the trigonometric calculation.