MHB Solve Triangle Height without Trig - Help for Kids

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To solve for the height of a triangle without using trigonometry, one can calculate the area using the formula area = base * height / 2. In this case, the area is determined to be 24 by using a base of 6 and a height of 8. By rearranging the area formula, the height can be found as h = 4.8 when using a base of 10. Alternatively, similarity can be applied, leading to the same height calculation of 4.8 through proportional relationships. This approach provides a straightforward solution suitable for students not yet familiar with trigonometry.
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View attachment 1801 My daughter was given this problem in an exam. She could not do it and was never given the solution. I can do the problem using trig but she has not been taught trig yet. She says that it can be done without trig using a more simple method that she doesn't know. Could somebody please explain how it could be done without using trig. It would be most appreciated :confused:
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Hello.

Lo that I think simplest is:

area=\dfrac{6*8}{2}=24

By placing the right triangle to another position.

Then:

24=\dfrac{10*h}{2}

h=4.8

Regards.
 
Another method would be to use similarity.

$$\frac{h}{6}=\frac{8}{10}$$

$$h=\frac{48}{10}=4.8$$

or

$$\frac{h}{8}=\frac{6}{10}$$

$$h=\frac{48}{10}=4.8$$
 
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