Answer:
10.5 feet
Step-by-step explanation:
In this problem, we have two similar triangles:
- One consists of the mailbox, its shadow and the hypothenuse
- The other one consists of the tree, its shadow and the hypothenuse
The two triangles are similar, so they have same proportions between their sides: therefore, we can apply the rule of three:
![\frac{m}{s_m}=\frac{t}{s_t}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%7D%7Bs_m%7D%3D%5Cfrac%7Bt%7D%7Bs_t%7D)
where
m = 36 in is the height of the mailbox
is the shadow of the mailbox
t is the height of the tree
is the length of the shadow of the tree
Solving for t, we find the height of the tree:
![t=\frac{m\cdot s_t}{s_m}=\frac{(36)(98)}{28}=126 in](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bm%5Ccdot%20s_t%7D%7Bs_m%7D%3D%5Cfrac%7B%2836%29%2898%29%7D%7B28%7D%3D126%20in)
And since
1 feet = 12 inches
The height of the tree in feet is
![t=\frac{126}{12}=10.5 ft](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B126%7D%7B12%7D%3D10.5%20ft)