Finding triangle height without trigonometry

[ter27]

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
View attachment 1802

 

[mente oscura]

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.

 

[MarkFL]

Another method would be to use similarity.

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

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

or

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

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