Answer: the height of the tree is equal to the distance from the tree to the point where you’re measuring, which is 47 feet. Therefore, the height of the tree is approximately 47 feet.
To find the height of the tree, we can use trigonometry, specifically the tangent function, since we have the angle of elevation and the distance from the tree. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the tree, in this case) to the adjacent side (the distance from the tree).
Given:
Angle of elevation ((\theta)) = 45°
Distance from the tree ((d)) = 47 feet
The tangent of 45° is 1, which means that the height of the tree ((h)) is equal to the distance from the tree ((d)).
So, using the formula: [ \tan(\theta) = \frac{h}{d} ]
We get: [ \tan(45°) = \frac{h}{47} ] [ 1 = \frac{h}{47} ] [ h = 47 ]
Therefore, the height of the tree is 47 feet, to the nearest foot.
