Question

A 18 foot ladder is leaning against a wall as shown

Express h in terms of θ
h(θ)=
Express θ in terms of h
θ(h)

Answer 1

I'm guessing the diagram shows a ladder leaning against a wall, making a right angle triangle with respect to the ground and the wall.

So, the wall's height is going to be the 'h', which will also be the 'opposite side' from the angle ϴ which is made from the ladder and the ground.
The ladder's length (18 foot) is going to be the 'hypotenuse' side and the other remaining side will be the 'adjacent'.

Now, once you've sorted out which side is which, we have to find the h (opp), and according to SOH CAH TOA, we will choose Sinϴ = opp/hyp.
so Sinϴ = h/18....now we gotta find h, so 'cross multiply' the equation to get h = 18 x sinϴ.

To find angle ϴ, simply take the inverse of Sinϴ= h/18... and you'll get ϴ = sin-1 (sin inverse) h/18

Hope this helps