Question

A 98ft extension ladder rests the top of a hook and ladder truck with its base 11 from the ground. The angle of elevation 73 degrees. How high up on the building is the ladder?

Answer 1

Answer:

∴ The height of the end of the ladder is $104.7178$

Step-by-step explanation:

Given,

The length $98$ feet and which is touch $11$ feet from the base and the angle of elevation $73$ degrees.

From the figure $\bigtriangleup ABC$ ;

$AC=98$ feet , $CE=11$ and $\angle ACB=73$ degree

Now from figure we have,

$Sin73=\frac{AB}{AC}$

Plug $AC$ value in above equation,

$Sin73=\frac{AB}{98}$

$AB=98\times Sin73$

$AB=93.7178$

$BD=CE$  ( from figure )

$BD=11$  

Then,

$AD=AB+BD$

$AD=93.7178+11$

$AD=104.7178$

Then the height of the end of the ladder is $104.7178$