Question

Question #06927

Answer 1

I found `195.7m` but I am not really sure of my method. Anyway check it and also check my maths!!!

Explanation:

Ok it is in Geometry but I had to use trignometry as well.
The object is a kind of wedge and I used this picture as well:

I first consider the two triangles ( I assume them right triangles in C) CPA and CPB and using trigonometry I say that:
`H=Q sin(57^@)`
`H=S sin(31^@)`
`CA= S cos(31^@)`
`CB= Q cos(57^@)`

Where `Q and S` are the hipotenuses.
Then I consider triangle ABC (right at B) and apply and Pythagoras Theorem to get:
`CA^2=AB^2+BC^2`
or:
`S^2 cos^2(31^@)=300^2+Q^2 cos^2(57^@)` (1)
BUT:
`H=Q sin(57^@)`
`H=S sin(31^@)`
so that:
`Q=H/ sin(57^@)`
`S=H/ sin(31^@)`
that substituted into (1) give:
`H^2/ sin^2(31^@)cos^2(31^@)=300^2+H^2/ sin^2(57^@) cos^2(57^@)`
rearranging:
`H^2[cos^2(31^@)/sin^2(31^@)- cos^2(57^@)/sin^2(57^@)]=300^2`
doing some calculations I got:
`H^2=300^2/2.348`
`H=195.7`