Answer:
h = 7.47 m
Step-by-step explanation:
According to the question, we have a right triangle formed by the ladder with the wall and the floor.
The length of the ladder is the hypotenuse and the desired height is the opposite. This is due to the fact that "the ladder makes an angle of 21" 27" with the horizontal". Then, the trigonometric ratio to use is sine:
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Using the values given:
[tex]sin(\21"27")=\frac{h}{14.5}[/tex]
Multiplying both sides by 14.5:
[tex]14.5*sin(\21"27")=14.5*\frac{h}{14.5}[/tex]
[tex]14.5*sin(\21"27")=h[/tex]
Then h = 7.47 m
