The legs of a right triangle are 15 and 20 find their projection onto the hypotenuse.

Let us determine what the hypotenuse will equal, when from the condition of the task we know that one leg is equal to 15 conventional units, and the second 20 conventional units:

√ (15 ^ 2 + 20 ^ 2) = √ (225 + 400) = √625 = 25.

Let’s determine what the half-perimeter of the figure will be:

(25 + 15 + 20): 2 = 30.

Let’s determine what the area of this figure will be equal to:

√ (30 (30 – 20) (30 – 25) (30 – 15)) = √ (30 * 10 * 5 * 15) = √22500 = 150.

Let’s determine what the height will be equal to:

150 * 2: 25 = 12.

Let’s define the projection of the smaller leg:

√ (15 ^ 2 – 12 ^ 2) = √81 = 9.

Let’s define the projection of the larger leg:

25 – 9 = 16.

Answer: 9 and 16.