# According to the diagram, what is the altitude?

## Feb 12, 2018

300 meters

#### Explanation:

Use the Pythagorean Theorem, ${a}^{2} + {b}^{2} = {c}^{2}$

In his case, you know a and c and need to find b . The names of the sides is really immaterial, but c is always the hypotenuse (the longest side).

So, ${400}^{2} + {b}^{2} = {500}^{2}$

Then, $160000 + {b}^{2} = 250000$

${b}^{2} = 250000 - 160000$

${b}^{2} = 90000$

Then $b = \pm \sqrt{90000} = 300 m$

Note that the answer has to be positive because it's a distance.

Feb 12, 2018

The altitude is 300 m.

#### Explanation:

if you name the triangle as ABC, where $\angle A = {90}^{\circ}$, then

By applying Pythagoras theorem,

${\left(\text{height")^2 +("base")^2=("hypotenuse}\right)}^{2}$

${\left(\text{height")^2=("hypotenuse")^2-("base}\right)}^{2}$

or,

${\left(\text{height}\right)}^{2} = {\left(500\right)}^{2} - {\left(400\right)}^{2}$

Thus,

$\text{height} = \sqrt{250000 - 160000}$

"height" = sqrt(90000) =color(red)("300 m")