Question

3. Consider the diagram below.

580
435
с
b
Determine the values of a, b, and c.

Answer 1

a = 664.5

b = 502.3

c = 767.3

Explanation:

Well, there are a couple of theorems that will help us do this problem

1. Given a right triangle and altitude to the hypotenuse, then the altitude is the mean proportion between the segments of the hypotenuse. That means in your problem that

`(435)/(b) = (b)/(580)`

`b^(2) = 435(580) = 252300\\b = √(252300) \\b = 502.3`

2. A leg of the triangle is the mean proportional between the hypotenuse and the segment adjacent to the leg. That means in your problem that

`((435 + 580))/(c) = (c)/(580) \\c^(2) = 1015(580) = 588700\\c = √(588700) \\c = 767.3`

`(1015)/(a) = (a)/(435) \\a^(2) = 1015(435) = 441525\\a = √(441525) \\a = 664.5`

See how easy it is if you know the theorems.

You could check your results by substituting a and into
`a^(2) + c^(2)` and see if you get get the square of the hypotenuse