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Type: Open-Ended
Category: Triangles
Level: Grade 11
Author: nsharp1
Created: 4 years ago

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Triangles Question

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For

$Delta ABC$ , as seen below, let the intersection of the altitude from vertex

$B$ and side

$bar{AC}$ be point

$D$ (not labeled). Also, let

$b = AC, \ c=AB, \ a = BC, \ x = AD, \ y=CD$ , and

$h = BD$ . Finally, let

$P = a+b+c$ and

$s=P/2$ .

The area of this triangle can be expressed using Heron's formula,

$A_{Delta ABC} = sqrt(s(s-a)(s-b)(s-c))$ , where

$s = (a+b+c)/2$ . The following questions will derive this formula.

Acute Triangle Height v2

Grade 11 Triangles

Rearrange the equation created in the previous question, so that

$y$ is isolated. Referring to the two equations created using the Pythagorean Theorem, rearrange one of them so that

$x$ is isolated. Now, using these three equations (the rearranged equation relating

$x$ and

$y$ , the rearranged equation created using the Pythagorean Theorem, and the other equation created using the Pythagorean Theorem), create an equation that has no

$x$ or

$y$ variables. Simplify the equation and isolate the

$h^2$ variable.