We are given that Imani needs to determine the height of a tree. She holds a 45^(∘) triangle so that one leg is horizontal and she sights the top of a tree along the hypotenuse. We also know that she stands 6 yards from the tree and her eyes are 5 feet from the ground.
First, let's convert yards to feet. Recall that there are 3 feet in each yard.
6yd=6*3ft=18ft
Let's add this information to our diagram. Notice that a 45^(∘) triangle is a rightisosceles triangle. Therefore, the legs of this triangle are congruent.
As we can see, the height of the tree is the sum of 18 and 5.
18+5=23
The height of the tree is 23 feet.
