Hello, r_maths!
You're doing fine! Code:
C
*
*| *
* | *
* | *
* |h *
* | *
* | *
* α | β *
A * * * * * * * * * * * * * B
D
In right triangle CDA: .tanα = h/AD . → . AD = h/tanα
In right triangle CDB: .tanβ = h/DB . → . DB = h/tanβ
. . . . . . . . . . . . . . . . . . . . h . . . . h
Then: .AB .= .AD + DB .= .------ + ------
. . . . . . . . . . . . . . . . . . . tanα . . tanβ
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
For part (b), we have:
. . . . . . . . h . . . . .h . . . . h搾osβ . . h搾osα
. . AB .= .------ + ------ .= .-------- + --------
. . . . . . . tanβ . . tanα . . . .sinβ . . . . sinα
. . . . . . .h新inα搾osβ + h新inβ搾osα . . . .h(sinα搾osβ + sinB搾osα)
. . . . = .-------------------------------- .= .------------------------------
. . . . . . . . . . . . sinα新inβ . . . . . . . . . . . . . . sinα新inβ
. . . . . . .h新in(α + β)
. . . . = .---------------
. . . . . . . .sinα新inβ
Edit:Too slow . . again