How high is a tree that casts a 33 foot shadow at the same time a 6 foot pole casts a 4 foot shadow?
Use a proportion. Cross multiply and solve for x.
x/33 = 6/4
33/h = 6/4
sorry
h/33 = 6/4 = height/shadow
33/×=6/4 cross multiply
33×4=132
6××=6×
132÷6=22
22=×
To determine the height of the tree, we can use a proportion based on the similar triangles created by the shadow of the tree and the pole.
Let's assign variables to the measurements:
- Height of the tree (x)
- Length of the shadow of the tree (33 feet)
- Height of the pole (6 feet)
- Length of the shadow of the pole (4 feet)
We can set up the proportion:
Height of Tree / Length of Tree's Shadow = Height of Pole / Length of Pole's Shadow
x / 33 = 6 / 4
Now, we can solve for x by cross-multiplying:
4x = 6 * 33
4x = 198
Divide both sides of the equation by 4:
x = 198 / 4
x = 49.5
Therefore, the height of the tree is 49.5 feet.