Answer :
By using trigonometry, it can be calculated that-
Distance from the top of the tree to the tip of the shadow is 15.46 feet
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions
[tex]sin \theta, cos \theta, tan \theta, cot \theta, sec \theta, cosec \theta[/tex]
[tex]sin \theta = \frac{Perpendicular}{Hypotenuse}\\\\cos \theta = \frac{Base}{Hypotenuse} \\\\tan \theta = \frac{Perpendicular}{Base} \\\\cot \theta = \frac{Base}{Perpendicular} \\\\sec \theta = \frac{Hypotenuse}{Base} \\\\cosec \theta = \frac{Hypotenuse}{Perpendicular} \\\\[/tex]
Let the angle of elevation be [tex]\theta[/tex] and distance from the top of the tree to the tip of the shadow be d feet
Here the tree represents the perpendicular, shadow represents the base and distance from the top of the tree to the tip of the shadow represents the hypotenuse
A tree that is 15 feet tall casts a shadow that is 4 feet long
[tex]tan\theta = \frac{15}{4}\\\theta = tan^{-1}( \frac{15}{4})\\\theta = 75.1^{\circ}[/tex]
Now,
[tex]sin75.1^{\circ} = \frac{15}{d}[/tex]
[tex]0.97 = \frac{15}{d}\\d = \frac{15}{0.97}\\d = 15.46 \ feet[/tex]
Distance from the top of the tree to the tip of the shadow is 15.46 feet
To learn more about trigonometry, refer to the link
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