Finding the Altitude to the Hypotenuse
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12. In the diagram below, $\Delta RST$ is a $3 - 4 - 5$ right triangle. The altitude, $h$, to the hypotenuse has been drawn. Determine the length of $h$.
This question includes visual content: A right triangle RST is shown with sides labeled 3, 4, and 5 (the hypotenuse). An altitude labeled 'h' is drawn from vertex T to the hypotenuse RS, creating two segments labeled 'b' and 'a'. A right-angle symbol is marked at vertex T and at the point where the altitude meets the hypotenuse.
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Hi Joshua, let's solve this geometry problem together. We need to find the length of the altitude h in this right triangle.
Finding the Altitude of a Right Triangle
We are given triangle RST with a right angle at vertex T. The legs are three and four, and the hypotenuse is five.
A very elegant way to solve this is by using the area of the triangle.
First, we can calculate the area using the two legs, three and four, which are perpendicular to each other.
Three times four is twelve, and half of that is six. So the area is six square units.
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