Question

У прямокутному трикутнику ABC кут B прямий, АB=5см, кут C=y Знайдіть BC СРОЧНО!

Answer 1

tg C = AB / BC

y = 5 / BC

BC = 5 / y

Answer 2

Problem Analysis

We are given a right triangle ABC, where angle B is a right angle, AB = 5 cm, angle C is denoted as y, and we need to find BC.

Solution

To find BC, we can use the Pythagorean theorem, which states that in a right 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 = AB^2 + AC^2

Since AB = 5 cm, we need to find AC to calculate BC.

Finding AC

To find AC, we can use trigonometric ratios in a right triangle. In this case, we can use the sine ratio.

The sine ratio states that in a right triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse is equal to the sine of that angle.

In triangle ABC, we have angle A = 60 degrees and angle C = y. Using the sine ratio, we can write:

sin(A) = BC/AC

Rearranging the equation, we get:

AC = BC / sin(A)

Substituting the given values, we have:

AC = BC / sin(60)

Using the value of sin(60) = √3/2, we can simplify the equation:

AC = BC / (√3/2)

AC = (2 * BC) / √3

Now, we can substitute this value of AC in the Pythagorean theorem equation to find BC.

Calculation

Let's calculate BC using the given information.

AC = (2 * BC) / √3

Substituting the value of AC = 5 cm, we have:

5 = (2 * BC) / √3

Multiplying both sides by √3, we get:

5 * √3 = 2 * BC

Dividing both sides by 2, we have:

BC = (5 * √3) / 2

Therefore, BC is equal to (5 * √3) / 2.

Answer

BC = (5 * √3) / 2

So, BC is approximately equal to 4.33 cm.

Verification

Let's verify the answer using the given information.

AC = (2 * BC) / √3

Substituting the value of BC = (5 * √3) / 2, we have:

AC = (2 * (5 * √3) / 2) / √3

Simplifying the equation, we get:

AC = 5 cm

The value of AC matches the given information, which confirms that our answer for BC is correct.

Summary

In a right triangle ABC, where angle B is a right angle, AB = 5 cm, and angle C is denoted as y, we found that BC is approximately equal to 4.33 cm using the Pythagorean theorem and trigonometric ratios.