Question

Geeta is 56 install and her shadow is 52 inches long.If a tree casts a 10 feet 10 inch long shadow under the same conditions,What is the actual height of the tree?

explain step by step......​

Answer 1

Answer:

The actual height of tree is 10 feet 81 inches

Step-by-step explanation:

Given as :

The height of Geeta = H = 56 inches

The measure of her shadow = X = 52 inches

According to question

So, Tan angle = $\dfrac{\textrm perpendicular}{\textrm base}$

Or, Tan angle = $\dfrac{H}{X}$

or, Tan angle = $\dfrac{\textrm 56 inches}{52 inches}$

or, Tan angle = 1.076              ........1

Again

Under the same condition

The height of tree = h = 10 feet 10 inches = 120 inches + 10 inches

i.e  h = 130 inches

Let The measure of shadow of tree = x inches

So, Tan angle = $\dfrac{\textrm perpendicular}{\textrm base}$

Or,  Tan angle = $\dfrac{h}{x}$

Or,  Tan angle = $\dfrac{130}{x}$

From Eq 1

1.076 = $\dfrac{130}{x}$

∴   x  = $\dfrac{130}{1.076}$

i.e  x = 120.81 inches

So, The measure of shadow of tree = x = 120 .81 inches

Since 1 feet = 12 inches

So, 120 inches = 12 feet

Hence, The actual height of tree is 10 feet 81 inches Answer

Answer 2

Answer:

actual height of tree is 10 feet 81 inches

Step-by-step explanation:

Given as :

The height of Geeta = H = 56 inches

The measure of her shadow = X = 52 inches

According to question

So, Tan angle = \dfrac{\textrm perpendicular}{\textrm base}

base

perpendicular

Or, Tan angle = \dfrac{H}{X}

X

H

or, Tan angle = \dfrac{\textrm 56 inches}{52 inches}

52inches

56inches

or, Tan angle = 1.076 ........1

Again

Under the same condition

The height of tree = h = 10 feet 10 inches = 120 inches + 10 inches

i.e h = 130 inches

Let The measure of shadow of tree = x inches

So, Tan angle = \dfrac{\textrm perpendicular}{\textrm base}

base

perpendicular

Or, Tan angle = \dfrac{h}{x}

x

h

Or, Tan angle = \dfrac{130}{x}

x

130

From Eq 1

1.076 = \dfrac{130}{x}

x

130

∴ x = \dfrac{130}{1.076}

1.076

130

i.e x = 120.81 inches

So, The measure of shadow of tree = x = 120 .81 inches

Since 1 feet = 12 inches

So, 120 inches = 12 feet

Hence, The actual height of tree is 10 feet 81 inches Answer