Question

To find the height of a tree, Wyatt places a mirror so that he can see the top of the tree in the mirror. The mirror is 3 ft from him and 7.5 ft from the tree. If Wyatt is 5.5 ft tall, how tall is the tree?
How would I solve this?

Answer 1

Since the angle of incidence is equal to the angle of reflection in the mirror you have tow similar right-angled triangles.
Thus we can use our good ol' fashioned ratios

x/7.5 = 5.5/3
3x = 41.25
x = 13.75
or 13.8 ft to the nearest tenth of a foot

Answer 2

For this you have to set up a ratio of:

3/7.5=5/x
you then cross multiply 3 with x and 7.5 with 5 which gives you
3x=37.5
then divide by 3
x=12.5 ft or 12 ft 6in