Question

to estimate the height of a tree, tia and felix walk away from the tree until the angle of sight with the top and bottom of the tree is a right angle. let h represent the height of a person’s eyes and d represent the distance away from the tree. answer parts a to c below.
the height of the tree is about 5.51 meters.
(type an integer or decimal rounded to the nearest hundredth as needed.)
b. if the height of felix’s eyes is 1.7 m, about how far from the tree is felix if his angle of sight is a right angle?
felix is about
from the tree.
(type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation:

Step1: Define right triangle sides

The vertical side (height from Felix's eyes to tree top) is $h - 1.7 = 5.51 - 1.7 = 3.81$ m. The horizontal side is distance $d$, and the line of sight is the hypotenuse (right angle between them, so we use tangent).

Step2: Set up tangent formula

For a right angle, the angle of sight to the top is $45^\circ$ (since the triangle is right isosceles when the angle of sight forms a right angle with the vertical/horizontal? No, correction: right angle between line of sight and tree, so $\tan(45^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{d}{3.81}$. Since $\tan(45^\circ)=1$,
$d = 3.81 \times 1$

Answer:

3.81