Answer:
1. Lets say the student is 10 feet away from the tree. We can make a right triangle from the base of the tree, to his feet, to the top of the tree. Lets say the angle made from the base of the tree to his feet to the top of the tree equals 51°. We can use the angle and the distance between him and the tree to calculate the height.We have the length of the side adjacent to the angle and we are looking for the height which is the length of the side opposite of the angle. We will have to use the tangent [tex](\frac{opposite}{adjacent})[/tex] of the angle to solve. So the tangent of 51 degrees is equal to the height divided by 10.
2. Solve for the length of the side opposite of the angle.
[tex]h=[/tex] height
[tex]tan(51)=\frac{h}{10}\\10*tan(51)=\frac{h}{10} *10\\12.34897157=h\\h=12 ft.[/tex]
The tree is approximately 12 feet tall.
