There is a tall tree in iva’s backyard. she thinks it might hit her house if it fell over. she measures that the base of the tree is 50 feet from her house. when iva stands at the edge of her house, the angle of elevation from her feet to the top of the tree is 50°. iva’s house is safe if the tree’s height is less than the tree’s distance from the house. complete the statement based on this information.
the height of the tree feet, so iva’s house is
answer choices:
1. greater than, less than, equal to
2. safe, not safe

The height of the tree is Greater than 50 feet, so Iva’s house is not safe

Step-by-step explanation:

step 1

Find the height of the tree

Let

h > the height of the tree

we know that

The tangent of angle of 50 degrees is equal to divide the opposite side to the angle of 50 degrees (height of the tree) by the adjacent side to the angle of 50 degrees (tree’s distance from the house)

so

tan(50°)=h/50

h=(50)tan(50°)=59.6 ft

therefore

The height of the tree is Greater than 50 feet, so Iva’s house is not safe

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed