Emily (who is 5.5 feet tall) wants to measure the height of a tree in the

forest near where she lives since there is a big storm approaching and she

is worried that it might fall over and hit her house if it is too tall. If she can

see the top of the tree at an angle of 46.4 degrees and if she estimates the

distance between her house and the tree to be 100 feet, is the tree tall

enough to hit her home?

YES

Explanation:

Here apply the formula for tangent of an angle to find height of the tree

Distance from house to tree is 100 ft = adjacent side

Tan ∅ = opposite side/adjacent side

Tan 46.4° = height of tree/100

h = 100 tan 46.4° = 105.01 ft

Given height of Emily is 5.5 ft, add this to 105.01 to find total height of the tree

=105.01 + 5.5 = 110.51 ft

The tree is tall (110.51 ft) enough to hit her home which is 100 ft away from the tree.