John is trying to determine the height of a tree that is in his yard. He notices that if he stands 12 feet from the tree, the tip of his shadow and the tip of the shadow of the tree are at the same place. Jon is 6 feet tall and his shadow at that time of day is 8 feet long. Part A. How long is the shadow of the tree at that time of day? Part B. Using the given information and your answer to Part A, determine the height of the tree. Show your work. Part C. Explain the geometric properties that allowed you to determine the answer for Part B.

If Jon's shadow is 8 feet long and he is 12 feet from the tree when their shadows touch, the tree's shadow must be 4 feet long. This means that the tree is half Jon's height, or 3 feet tall. Hope this helps!

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ap8997154 ap8997154 · Answer 2 · 2022-07-23T09:10:40+02:00

The geometric property that allowed you to determine the answer for Part B is the Tangent property of trigonometry, which is the ratio of the perpendicular side and the base side of the triangle.

What is Tangent (Tanθ)?

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The diagram for the given situation can be modelled as shown below.

A.) The length of the tree's shadow is the sum of the distance between the tree and John, and the length of the shadow. Therefore, the length of the shadow of the tree is,

BC = 12 feet + 8 feet = 20 feet

B.) The height of the tree can be written can be found using the tangent ratio. Therefore, the tangent ratio for ∠C in the ΔABC and ΔEDC can be written as,

tan(θ) = AB/BC = ED/DC

Height of the tree/ (12 + 8) = 6/8

Height of the tree = 15 meters

C.) The geometric property that allowed you to determine the answer for Part B is the Tangent property of trigonometry, which is the ratio of the perpendicular side and the base side of the triangle.

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

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