Find the height of any triangle?

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Homework Help Overview

The original poster presents a problem involving a triangle with known side lengths: a base of 190 ft, side A of 182 ft, and side B of 363 ft. The goal is to determine the height of the triangle based on this information.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants suggest various methods for finding the height, including using the law of sines or cosines, drawing a diagram, and setting up equations based on the apex's distance from the corners. Some express uncertainty about the formulas and emphasize the importance of visual representation.

Discussion Status

The discussion is active with multiple approaches being explored. Participants are sharing different strategies and emphasizing the necessity of drawing a diagram to aid understanding. There is no clear consensus on a single method yet.

Contextual Notes

Participants note the importance of visualizing the triangle, indicating that a diagram may help clarify the relationships between the sides and angles. There is also a suggestion that the original poster may need to consider additional geometric properties to proceed.

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Homework Statement



I have the side lengths of a triangle. The base is 190 ft long, side A is 182 ft long and side B is 363 ft long. That's all I know.

Homework Equations





The Attempt at a Solution



I know these side lengths are related somehow.
 
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I'm not 100% sure this is the formula, but try this:
[itex]h=\frac{2}{c}\sqrt{s(s-a)(s-b)(s-c)}[/itex]
where
[itex]s=\frac{a+b+c}{2}[/itex]
 
Draw the picture, use the law of sines or cosines to find the angle measures, drawn an altitude, calculate.
 
Or you could use the fact that you know the distance of the apex from the other two corners to find two equations in x and y.
 
Use the law of cosines to find the angle opposite side B first.
 
DRAW THE DAMN PICTURE. All of the other suggestions here are good but if you don't start off by drawing a reasonable picture of what you're working with, you're shooting in the dark.
 
phinds said:
DRAW THE DAMN PICTURE. All of the other suggestions here are good but if you don't start off by drawing a reasonable picture of what you're working with, you're shooting in the dark.
Very true !
 

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