Find the ratio of the legs, the height and projection of the legs to the hypotenuse, if the hypotenuse of a right

Find the ratio of the legs, the height and projection of the legs to the hypotenuse, if the hypotenuse of a right triangle is 26 cm, and one of the legs is 10 cm.

We find out what value will be equal to the length of the other leg:

√ (26 ^ 2 – 10 ^ 2) = √ (16 * 36) = 24.

Then the ratio of the legs:

10:24 = 5:12.

Answer: The ratio of legs is 5 to 12.

Now we can find what the height will be equal to, which is drawn to the hypotenuse:

Str = 1/2 * 10 * 24 = 120;

120: 26/2 = 240/26 = 9 6/26.

Answer: The height is 9 6/26 cm.

Now let’s calculate what the projections of the legs on the hypotenuse will be:

√ (10 ^ 2 – (240/26) ^ 2) = 100/26;

26 – 100/26 = 576/26.

Answer: The projections of the legs are 100/26 cm and 576/26 cm.