Question

A tree is "x"meters high. The angle of elevation of its top from a point P on the ground is 23degrees. Form another point Q, 10meters from P and in line with P and the foot of the tree, the angle of elevation is 32degrees. Find "x".

(Please don't give me the answer only.. I also need the way so I can learn from it. Thankyou :])

Answer 1

Make a neat diagram.
Label the bottom of the tree R and its top T
You should have two right angled triangles, PTR and QTR
Label PQ = 10, let QR = x and RT = h

In triangle QRT, tan 32º=h/x
h = xtan32

in triangle PTR, tan 23º = h/(x+10)
so h = (x+10)tan23

equate the two equations, (both are h=...)
xtan32 = (x+10)tan23
xtan32 = xtan23 + 10tan23
xtan32 - xtan23 = 10tan23
x(tan32-tan23) = 10tan23

x = 10tan23/(tan32-tan23)

Now you could solve for x now, and sub that back into
h = xtan32

I got h = 13.24, let me know if you got the same answer.