Question

An inclined plane rises 1 in 10.If length of the inclined plane is 5 m , calculate the height of the raised end above the horizontal

Answer 1

Answer: The height is $\frac { 5 }{ \sqrt { 101 } } meter$

Given:

Inclined plane rises in 1 in 10.Length = 5 m

height = ?

Solution:

$tan\quad \theta \quad =\quad \frac { 1 }{ 10 }$

$sin\quad \theta \quad =\quad \frac { 1 }{ \sqrt { { 10 }^{ 2 }\quad +\quad { 1 }^{ 2 } } } =\frac { 1 }{ \sqrt { 101 } }$

$sin\quad \theta \quad =\quad \frac { h }{ 5 }$

$\frac { h }{ 5 } =\frac { 1 }{ \sqrt { 101 } }$

$h\quad =\quad \frac { 5 }{ \sqrt { 101 } } meter$

Answer 2

Answer:

$\bf\textbf{Hence, The height of the raised end = }\frac{5}{\sqrt{101}}$

Step-by-step explanation:

Length of the inclined plane = 5 m

As the inclined plane rises from 1 to 10

$\implies \sin\theta=\frac{1}{\sqrt{10^2+1^2}}\\\\\implies\sin\theta=\frac{1}{\sqrt{101}}$

Now, let the height of the raised end above the horizontal be h m

$\implies \frac{h}{5}=\frac{1}{\sqrt{101}}\\\\\implies h=\frac{5}{\sqrt{101}}$

$\bf\textbf{Hence, The height of the raised end = }\frac{5}{\sqrt{101}}$