ABC is a right-angled triangle. angle A = 90 degrees Side AB = 8, side AC = 17.

ABC is a right-angled triangle. angle A = 90 degrees Side AB = 8, side AC = 17. AD – perpendicular lowered to the side of the BC. find BD-?

Let us determine what the second leg of the triangle ABC will equal, when from the condition of the task we know that the length of the side AB is 8, and the length of the side of the AC is 17:

√ (17 ^ 2 – 8 ^ 2) = √ (9 * 25) = 3 * 5 = 15.

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

1/2 * 8 * 15 = 60.

Let us determine what the height AD will be equal to in this case:

60 * 2: 17 = 120/17.

Let us determine what the length BD will be equal to in this case:

√ (8 ^ 2 – (120/17) ^ 2) = √ (64 – 14400/289) = √ (4096/289) = 64/17.

Answer: The length BD is 64/17.