Question

Help please triangles and trig

Answer 1

Given:

A figure of a right angle.

To find:

The value of x.

Solution:

We know that the measure of the altitude on the hypotenuse of a right right triangle is the geometric mean of the segments of the hypotenuse.

If the altitude "h", divides the hypotenuse in two segments "a" and "b", then

`h=√(ab)`

In the given figure, the measure of the altitude is x and it divides the hypotenuse in two segments 3 units and 24 units.

Using the above theorem, we get

`x=√(3* 24)`

`x=√(72)`

`x=6√(2)`

Therefore, the required solutions for the given blanks are:

Blank 1: 72

Blank 2: 6

Blank 3: 2