The legs of a right-angled triangle ABC are 9 and 12, the hypotenuse is 15. What is the Height (h) drawn to the hypotenuse.

Let us express one of the segments into which the height of the hypotenuse is divided, for which we use the variable a.

Then the second segment can be written by us as 15 – a.

Therefore, the square of the height in a triangle with a hypotenuse of 9 can be expressed as 9 ^ 2 – a ^ 2, in a triangle with a hypotenuse of 12 as 12 ^ 2 – (15 – a) ^ 2.

Let’s make the equation:

9 ^ 2 – a ^ 2 = 12 ^ 2 – (15 – a) ^ 2;

81 – a ^ 2 = 144 – 225 + 30a – a ^ 2;

30a = 16 ^ 2;

a = 5.4.

Let’s find out what the height is equal to:

√ (81 – 29.16) = √51.84 = 7.2.

Answer: It is equal to 7.2.