- #1

maros522

- 15

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## Homework Statement

We have triangle with sides d1,d2,l and angle [itex]\alpha[/itex] between d1 and d2.

Assume small change [itex]\Delta\alpha[/itex] of [itex]\alpha[/itex].

## Homework Equations

Then we can write for [itex]\Delta[/itex]l equation

[itex]\Delta[/itex]l=(d1*d2)/(l) * sin[itex]\alpha[/itex][itex]\Delta\alpha[/itex].

How can I prove that?

## The Attempt at a Solution

I start with function cos([itex]\alpha[/itex]+[itex]\Delta\alpha[/itex])=cos[itex]\alpha[/itex] * cos[itex]\Delta\alpha[/itex] - sin[itex]\alpha[/itex] * sin[itex]\Delta\alpha[/itex]

and laws of cossines [itex](l+\Delta l)^2[/itex]=[itex]d1^2[/itex]+[itex]d2^2[/itex]-2d1d2*cos([itex]\alpha[/itex]+[itex]\Delta\alpha[/itex])

But I don't know how to continue. :(