A ladder manufacturer recommends that its ladders be used on level ground at an angle of 72.5 degree to the horizontal. At that angle, how far up the side of a building will the top of a 14 foot ladder reach ? Round all side lengths to the nearest thousandth and round angle measures to the nearest degree.
Answer:
The height of building is 13.35 feet
Solution:
Height of ladder = 14 foot
Angle of 72.5 degree to the horizontal
We have to find the height of building
The ladder, ground and height of building forms a right angled triangle
The figure is attached below
ABC is a right angled triangle
AB = height of building = x
AC = height of ladder = 14 feet
Angle c = 72.5 degree
By defintion of sine,
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
[tex]sin 72.5 = \frac{AB}{AC}\\\\sin 72.5 = \frac{x}{14}\\\\0.9537 = \frac{x}{14}\\\\x = 14 \times 0.9537\\\\x = 13.35[/tex]
Thus height of building is 13.35 feet
