Question

22 БАЛЛА Высота AD треугольника ABC делит сторону BC на отрезки BD и CD так, что BD = 15 см, CD = 5 см. Найдите площадь S треугольника АВС, если ∠B = 30° . В ответе укажите

Answer 1

Ответ:

1) В тр-ке ABD катет AD=1/2 АВ. AD обозначим через х. АВ=2х.

По теореме Пифагора 4x^2-x^2=15^2; x=V75=5V3 - AD.

2) AC^2=AD^2+CD^23= 100; AC=V100=10.

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Answer 2

Ответ:10

Объяснение:В тр-ке ABD катет AD=1/2 АВ. AD обозначим через х. АВ=2х.По теореме Пифагора 4x^2-x^2=15^2; x=V75=5V3 - AD.2) AC^2=AD^2+CD^23= 100; AC=V100=10.

Answer 3

Calculation of the Triangle's Height

To find the height of triangle ABC, we need to use the properties of a right-angled triangle and the given information about the lengths of the segments BD and CD.

Let's denote the height of triangle ABC as h. Since triangle ABC is not specified to be a right-angled triangle, we can assume that the height is perpendicular to the base BC.

According to the given information, BD = 15 cm and CD = 5 cm. We can see that BD + CD = BC, which means that the sum of the lengths of the segments BD and CD is equal to the length of the base BC.

Using this information, we can set up the following equation:

BD + CD = BC

Substituting the given values, we have:

15 cm + 5 cm = BC

20 cm = BC

Now, we can use the properties of a right-angled triangle to find the height h. In a right-angled triangle, the height is the perpendicular drawn from the vertex of the right angle to the base.

Since angle B is given as 30°, we can use trigonometric ratios to find the height. The tangent of angle B is defined as the ratio of the length of the opposite side (h) to the length of the adjacent side (BD).

Using the tangent function, we can write:

tan(B) = h / BD

Substituting the given values, we have:

tan(30°) = h / 15 cm

Now, we can solve for h:

h = tan(30°) * 15 cm

Using a calculator, we find that tan(30°) is approximately 0.5774. Therefore:

h ≈ 0.5774 * 15 cm

h ≈ 8.661 cm

So, the height of triangle ABC is approximately 8.661 cm.

Calculation of the Triangle's Area

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

Area = (1/2) * base * height

In this case, the base of the triangle is BC, which we found to be 20 cm, and the height is h, which we found to be approximately 8.661 cm.

Substituting these values into the formula, we have:

Area = (1/2) * 20 cm * 8.661 cm

Using a calculator, we find that:

Area ≈ 86.61 cm²

Therefore, the area of triangle ABC is approximately 86.61 cm².