Question

У прямокутному трикутнику висота,проведена до гіпотенузи ,дорівнюе 5см.Проекції катетів на гіпотенузу відносяться як 1:25.Знайдіть ці проекції

Answer 1

H² = x'y',дзе х і у - праекцыі.Няхай х' = x,тады у' = 25x,таму што x'/y'=1/25;
5²=x²*25;x=1
x' = 1;y'=25

Answer 2

Given Information:

- The height of a right triangle drawn to the hypotenuse is 5 cm. - The projections of the legs onto the hypotenuse are in a ratio of 1:25.

Solution:

Let's denote the lengths of the legs of the right triangle as a and b, and the length of the hypotenuse as c.

We know that the height of the triangle drawn to the hypotenuse is 5 cm. This means that the area of the right triangle is equal to (1/2) * a * b = (1/2) * 5 * c.

We also know that the projections of the legs onto the hypotenuse are in a ratio of 1:25. This means that the lengths of the projections are (1/26) * c and (25/26) * c.

Using the Pythagorean theorem, we can express the lengths of the legs in terms of the hypotenuse:

a^2 + (1/26)^2 * c^2 = c^2 b^2 + (25/26)^2 * c^2 = c^2

Simplifying these equations, we get:

a^2 + (1/676) * c^2 = c^2 b^2 + (625/676) * c^2 = c^2

Rearranging the equations, we have:

a^2 = (675/676) * c^2 b^2 = (51/676) * c^2

Taking the square root of both sides, we find:

a = (sqrt(675)/26) * c b = (sqrt(51)/26) * c

Therefore, the projections of the legs onto the hypotenuse are:

Projection of a: (1/26) * c Projection of b: (25/26) * c

Let's calculate the values of the projections using the given information:

Projection of a: (1/26) * c = (1/26) * 5 = 0.1923 cm Projection of b: (25/26) * c = (25/26) * 5 = 4.8077 cm

So, the projections of the legs onto the hypotenuse are approximately 0.1923 cm and 4.8077 cm.

Please note that the above calculations are based on the given information and assumptions.