Question

$\huge\mathcal\blue{Question:-}$
At sunset, a tree projects a shade that is 2.5 meters of length. The distance from the tree top to the most distant end of the shade is 4 meters. What is height of the tree?

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Answer 1

$\color{red}{ \huge{\mathtt{{ Side = 3.12 \: \: m}}}}</p><p>$

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Given :-

• Tree projects the shade of = 2.5 m
• Distance from the tree top to the most distant end of the shade is 4 meters.

To find :-

• Height of the tree.

Let there is a right angled triangle :-

• With Base b, which is shade of the tree.
• Its height a , which is height of the tree
• Hypotenuse h, which is distance from the top of the tree to the end of the shade.

So, according to the question:-

• Since the triangle is right, we apply the Pythagorean theorem to calculate its height.

$\boxed{ \color{orange} \Large{ \mathtt{H² = A² + B²}}}$

$\mathtt{\implies{ {(4)}^{2} = {(a)}^{2} + {(2.5)}^{2} }}$

$\mathtt{\implies{ 16 = {a}^{2} = 6.25}}$

$\mathtt{\implies{ {a}^{2} = 16 - 6.25}}$

$\mathtt{\implies{ {a}^{2} = 9.75}}$

$\mathtt{\implies{ a = \sqrt{9.75} }}$

$\color{red}{ \large{\mathtt{\implies{ a = 3.12 \: \: m}}}}$

Therefore, side is 3.12 m.

Answer 2

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