A tree is growing 43-ft feet from a home. The home owner is worried the tree could fall onto the house during a storm and is considering having a tree service come out and cut it down. To determine if the tree needs to be cut down the home owner stands '15' feet from the tree and measures the angle between the ground and the top of the tree to be 71∘

If the height of the tree is greater than or equal to 43 feet then it will hit the house if it falls. To determine the height of the tree, use right triangle trig. We are looking for the height of the tree, so we will call that x. The base of the right triangle is 15, and the angle of elevation is 71. Since the height of the tree is the side opposite the base angle (angle of elevation), and the base of the triangle is adjacent to the base angle, we need the tangent ratio to find the height of the tree. Namely,

[tex]tan(71)=\frac{x}{15}[/tex] and

15 tan(71) = x

On yur calculator, that comes out to 43.56 feet or, rounded to the nearest foot, 44 feet. The tree will hit the house and needs to come down (or maybe just trimmed!)