Solve the system for h and x?

Question

tan (31 deg) = (h/x)
tan (24 deg) = (h/x+300)

I've tried substituting but I can't seem to be able to isolate x or h no matter what I do. Any help is greatly appreciated.

Answer 1

I'm guessing the second one should be h/(x+300), not h/x + 300.
Lets make h the subject of each.
h = x tan 31
h = (x+300) tan 24.
Equate those:
x tan 31 = (x+300) tan 24
x tan 31 = x tan 24 + 300 tan 24
x(tan 31 - tan 24) = 300 tan 24
x = 300 tan 24 / (tan 31 - tan 24).
You can then work out h = x tan 31.
You should get x = 858.2, h = 515.7, approx.

Answer 2

If it's on this form then just don't bother yourself !
h/x= 0.6 --> x=0.6h from the first equation
from the second
h/x+300= 0.4452 -->h/x=299.5548 ->h=299.5548x
x=0.6(299.554x)=179.732x

so x = 179.732x which is wrong for any value other than 0 which don't satisfy the equations..
The others made it clear how the system would be solved if there was an error in the eequations from the start.

Answer 3

if by this you mean

tan(31) = h/x
h = tan(31)x

tan(24) = h/(x + 300)
h = tan(24)(x + 300)

tan(31)x = tan(24)(x + 300)
tan(31)x = tan(24)x + 300tan(24)
tan(31)x - tan(24)x = 300tan(24)
x(tan(31) - tan(24)) = 300tan(24)
x = (300tan(24))/(tan(31) - tan(24))
x = about 858.234

h = about 515.679

ANS :
x = about 858
h = about 516