Question

Катети прямокутного трикутника дорівнюють 8 см. І 6 см. Обчислити висоту і медіана трикутника проведену з вершини прямого кута.

Answer 1

C- гiпотенуза, m- медіана, h- висота
По теоремі пифагора с^2=а^2+b^2
с^2=64+36=100
c=10
Mедіана, падаюча на гіпотенузу, дорівнює половині гіпотенузи
m=10/2=5
h=ab/c=8*6/10=4.8

Answer 2

Calculation of the Height and Median of a Right Triangle

To calculate the height and median of a right triangle, we need to use the given lengths of the triangle's legs. In this case, the lengths of the legs are 8 cm and 6 cm.

Let's start by calculating the height of the triangle. The height is the perpendicular distance from the right angle to the hypotenuse. To find the height, we can use the formula:

Height = (Leg1 * Leg2) / Hypotenuse

In this case, the lengths of the legs are 8 cm and 6 cm. Let's assume the hypotenuse is c cm. Using the formula, we can write:

Height = (8 cm * 6 cm) / c cm

To find the value of c, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:

8 cm^2 + 6 cm^2 = c cm^2

Simplifying the equation, we get:

64 cm^2 + 36 cm^2 = c cm^2

100 cm^2 = c cm^2

Taking the square root of both sides, we find:

c = 10 cm

Now that we know the value of c, we can substitute it back into the formula for the height:

Height = (8 cm * 6 cm) / 10 cm

Simplifying the equation, we get:

Height = 48 cm / 10 cm

Height = 4.8 cm

Therefore, the height of the right triangle is 4.8 cm.

Next, let's calculate the median of the triangle. The median is a line segment drawn from a vertex of the triangle to the midpoint of the opposite side. In a right triangle, the median drawn from the vertex of the right angle is also the hypotenuse.

In this case, the hypotenuse is 10 cm, as we calculated earlier. Therefore, the median of the triangle drawn from the vertex of the right angle is also 10 cm.

To summarize: - The height of the right triangle is 4.8 cm. - The median of the right triangle drawn from the vertex of the right angle is 10 cm.

Please let me know if there's anything else I can help you with!