Answer :
Given:
The length of the ladder = 12 ft
The angle of ladder with ground = 60 degrees
To find:
How far up the building the ladder will reach.
Solution:
Using the given information draw a figure as shown below.
We need to find the vertical distance between the top of ladder and the ground.
Let x be the required distance.
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the below triangle ABC,
[tex]\sin A=\dfrac{BC}{AC}[/tex]
[tex]\sin 60^\circ=\dfrac{x}{12}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{x}{12}[/tex]
Multiply both sides by 12.
[tex]\dfrac{\sqrt{3}}{2}\times 12=x[/tex]
[tex]6\sqrt{3}=x[/tex]
Therefore, the ladder will reach [tex]6\sqrt{3}[/tex] ft far up the building.
