Question

В треугольнике АВС, угол С=30 градусов, а высота ВН делит сторону АС на отрезки СН и НА соответственно равные 5 см и 7 см.найдите площадь треугольника АВС. помогите пожалуйста, срочно нужно!!!!даю 100 баллов!

Answer 1

Ответ: 10√3 см²

Объяснение: основная идея: против угла С, равного 30°, лежит катет ВН, равный половине гипотенузы СВ, катет ВН, он же и высота треугольника,  подлежит нахождению, например, по теореме Пифагора.

И ВТОРАЯ ЧАСТЬ : ПОЛОВИНА ПРОИЗВЕДЕНИЯ основания АС на высоту ВН- это искомая площадь ΔАВС.

далее - см. приложение

Answer 2

Solving for the Area of Triangle ABC

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

Area = (1/2) * base * height

Given information: - Angle C = 30 degrees - Height BH divides side AC into segments CH and HA, with lengths 5 cm and 7 cm respectively.

Calculating the Area

Using the given information, we can calculate the area of triangle ABC.

The base of the triangle, AC, is the sum of the segments CH and HA: AC = CH + HA

Now, we can use the formula for the area of a triangle: Area = (1/2) * base * height

Substitute the values: Area = (1/2) * (CH + HA) * BH

Now, we can calculate the area using the given values: Area = (1/2) * (5 cm + 7 cm) * BH Area = (1/2) * 12 cm * BH Area = 6 cm * BH

Finding the Height BH

To find the height BH, we can use trigonometric ratios in a right-angled triangle. Since angle C is 30 degrees, we can use the sine function to find BH.

The sine of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse: sin(C) = opposite/hypotenuse

In this case, BH is the opposite side, and AC is the hypotenuse.

Using the given angle C and the length of the opposite side CH, we can calculate the length of BH: sin(30 degrees) = CH/BH

Solving for BH: BH = CH / sin(30 degrees)

Substitute the value of CH (5 cm) and calculate BH: BH = 5 cm / sin(30 degrees) BH ≈ 10 cm

Calculating the Area (Final Step)

Now that we have found the length of BH, we can calculate the area of triangle ABC: Area = 6 cm * 10 cm Area = 60 cm²

Therefore, the area of triangle ABC is 60 square centimeters.