Question

Дано: трикутник ABC BD_|_AC AD=21см CD=27 см кут А =30 градусів Знайти :S трикутника ? * повний розв’язок *

Answer 1

Given Information:

We are given the following information about triangle ABC: - BD is perpendicular to AC. - AD = 21 cm. - CD = 27 cm. - Angle A = 30 degrees.

Solution:

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 AC and the height is BD.

To find the length of AC, we can use the Law of Cosines:

AC^2 = AD^2 + CD^2 - 2 * AD * CD * cos(A)

Substituting the given values:

AC^2 = 21^2 + 27^2 - 2 * 21 * 27 * cos(30)

Now we can calculate the length of AC:

AC = sqrt(21^2 + 27^2 - 2 * 21 * 27 * cos(30))

To find the height BD, we can use the formula for the height of a right triangle:

BD = AC * sin(A)

Substituting the values we have:

BD = sqrt(21^2 + 27^2 - 2 * 21 * 27 * cos(30)) * sin(30)

Finally, we can calculate the area of triangle ABC:

Area = (1/2) * AC * BD

Substituting the values we have:

Area = (1/2) * sqrt(21^2 + 27^2 - 2 * 21 * 27 * cos(30)) * sin(30) * sqrt(21^2 + 27^2 - 2 * 21 * 27 * cos(30))

Simplifying the expression:

Area = (1/2) * sqrt((21^2 + 27^2 - 2 * 21 * 27 * cos(30))^2) * sin(30)

Calculating the value:

Area = (1/2) * sqrt((21^2 + 27^2 - 2 * 21 * 27 * cos(30))^2) * 0.5

Therefore, the area of triangle ABC is (1/2) * sqrt((21^2 + 27^2 - 2 * 21 * 27 * cos(30))^2) * 0.5 square units.

Please note that the actual numerical value of the area cannot be determined without the specific values of AD and CD.