Question

ПОЖАЛУЙСТА ПОМОГИТЕ С КОНТРОЛЬНЫМ ЗАДАНИЕМ. СЕГОДНЯ НУЖНО СДАТЬ!!! Катеты прямоугольного треугольника =10см и 24см. Найти гипотенузу треугольника, длину высоты, опущенной на гипотенузу и проекции катетов на гипотенузу. ПОЖАЛУЙСТА, ПОМОГИТЕ!!!

Answer 1

Ответ:

См фото

Объяснение:

См фото

Answer 2

#### Finding the Hypotenuse of a Right Triangle To find the hypotenuse of a right triangle, you 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, the lengths of the two legs (or catheti) of the triangle are given as 10 cm and 24 cm. Let's calculate the length of the hypotenuse. Using the Pythagorean theorem, we have: **c^2 = a^2 + b^2** Where: - c is the length of the hypotenuse - a and b are the lengths of the legs Substituting the given values, we get: **c^2 = 10^2 + 24^2** Simplifying the equation: **c^2 = 100 + 576** **c^2 = 676** Taking the square root of both sides: **c = √676** **c = 26 cm** Therefore, the length of the hypotenuse of the triangle is **26 cm**. #### Finding the Length of the Altitude (Height) of the Triangle To find the length of the altitude (height) of the triangle, we can use the formula for the area of a right triangle. The area of a right triangle is given by: **Area = (1/2) * base * height** In this case, the base of the triangle is one of the legs, which is 10 cm. Let's calculate the length of the altitude. Rearranging the formula, we have: **Height = (2 * Area) / base** Since the triangle is a right triangle, the area can also be calculated using the formula: **Area = (1/2) * a * b** Substituting the given values, we get: **Area = (1/2) * 10 * 24** **Area = 120 cm^2** Substituting the area and base values into the formula for height, we have: **Height = (2 * 120) / 10** **Height = 24 cm** Therefore, the length of the altitude (height) of the triangle is **24 cm**. #### Finding the Length of the Projection of the Legs on the Hypotenuse To find the length of the projection of the legs on the hypotenuse, we can use similar triangles. In a right triangle, the projection of a leg onto the hypotenuse creates two similar triangles. The lengths of the projections are proportional to the lengths of the corresponding legs. Let's denote the projection of the first leg (10 cm) as x and the projection of the second leg (24 cm) as y. Using the proportionality of the similar triangles, we can set up the following equation: **x / 10 = y / 24** Cross-multiplying, we get: **24x = 10y** Simplifying the equation: **12x = 5y** Therefore, the length of the projection of the first leg (10 cm) on the hypotenuse is **12x** and the length of the projection of the second leg (24 cm) on the hypotenuse is **5y**. Please note that without additional information or specific values for x and y, we cannot determine the exact lengths of the projections. I hope this helps! Let me know if you have any further questions.