Lois C. answered • 05/15/20
BA in secondary math ed with 20+ years of classroom experience
If we draw a diagram for this, our right triangle will have the tree as the vertical leg, the shadow of 12 feet as the horizontal leg, and the angle formed by the horizontal leg and the hypotenuse will be 62°( note: this would be the "angle of elevation" of the sun). In relation to the 62° angle, the sides we are dealing with are the opposite and the adjacent. Therefore, we will set up an equation involving the tangent ratio to solve for the height of the tree. If we let "y" represent the tree height, the equation will be tan 62 = y/12. To isolate y, we multiply the value of tan 62 by 12, and this gives 22.5687 feet. Since the length of the shadow is given as whole feet, we can round the tree height the same way and call it approximately 23 feet in height.
