Answer:
6 feet
Step-by-step explanation:
Given,
The height of tree, say AB ( A is top, B is bottom ) = 36 foot,
Length of its shadow, BE = 60 feet,
Suppose CD represents me, ( where C is top, D is bottom )
We have, BD = 50 feet,
∵ DE = BE - BD = 60 - 50 = 10 feet,
Using trigonometric ratio,
[tex]\tan A = \frac{CD}{DE}=\frac{AB}{BE}[/tex]
[tex]\implies \frac{CD}{10}=\frac{36}{60}[/tex]
[tex]CD = \frac{36}{60}\times 10 =\frac{36}{6}=6[/tex]
Hence, I would be 6 feet tall.
You could stand at 6 feet and still be completely in the shadow of the tree.
Given
You are standing such that a 36-foot tree is directly between you and the sun.
If you are standing 50 feet away from the tree and the tree casts a 60-foot shadow.
Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion).
BC to be the height of the tree and DE to be the height of how tall you could be and still be completely in the shadow of the tree.
[tex]\rm \angle D= \angle B =90\ degress[/tex]
Therefore,
By the similar triangle property;
[tex]\rm \dfrac{DE}{BC} =\dfrac{AD}{AC}\\\\\dfrac{x}{36}=\dfrac{60-50}{60}\\\\\dfrac{x}{36}=\dfrac{10}{60}\\\\\dfrac{x}{36}=\dfrac{1}{6}\\\\6 \times x = 1 \times 36\\\\6x=36\\\\x = \dfrac{36}{6}\\\\x=6[/tex]
Hence, you could stand at 6 feet and still be completely in the shadow of the tree.
To know more about Similar triangles click the link given below.
https://brainly.com/question/1468337
