# Question 1fb7c

Nov 11, 2017

3.35 m (app)

#### Explanation:

Here Ladder formed hypotenuse with wall (height) and horizontal (base) with an angle of 60 degree. As per right angle triangle ;-
$\sin {60}^{\cdot}$ = height/hypotenuse = 3/hypotenuse.

$\frac{\sqrt{3}}{2}$ = 3/hypotenuse

Hypotenuse = 3 x 2/$\sqrt{3}$ = $2 \sqrt{3}$

As the height of the ladder is fixed, means hypotenuse is fixed. But the ladder slides which formed 75 degree and touched new height of the wall.

Again $\sin {75}^{\cdot}$ = new height /hypotenuse.

$\Rightarrow \frac{\sqrt{3} + 1}{2 \sqrt{2}}$ = new height/$2 \sqrt{3}$

$\Rightarrow \frac{2 \sqrt{3} \left\{\sqrt{3} + 1\right\}}{2 \sqrt{2}}$ = new height.

$\Rightarrow \frac{1.732 \left\{1.732 + 1\right\}}{1.414}$ = new height

So, new height = 3.35 m (app)

[NOTE : sin 75^* = sin(45+30)^* = sin 45 cos 30 + cos 45 sin 30 = 1/sqrt2. sqrt3/2 + 1/sqrt2. 1/2 = [sqrt3 + 1]/(2 sqrt2)#]