Answer:
See explanation
Explanation:
Given
Represent the vertical angle with [tex]\theta[/tex]
[tex]\theta = 75[/tex]
The question has incomplete details because the length of the ladder is not given; neither is the distance between the ladder and the wall given.
See attachment for illustration
So, this solution will be based on assumptions.
Represent
- The height from ground to the top of the ladder with y
- The length of the ladder with L
- The distance between the ladder and the wall with x
Carla could solve for y in any of the following ways:
1. Tan formula
[tex]tan \theta = \frac{opp}{adj}[/tex]
In this case:
[tex]tan \theta = \frac{x}{y}[/tex]
Multiply both sides by y
[tex]y * tan \theta = \frac{x}{y} * y[/tex]
[tex]y * tan \theta = x[/tex]
Divide both sides by tan
[tex]y = \frac{x}{tan \theta}[/tex]
[tex]y = \frac{x}{tan 75}[/tex]
This can be used if the distance (x) between the ladder and the wall is known.
Assume x = 15
[tex]y = \frac{15}{tan 75}[/tex]
[tex]y = 4.02[/tex]
2. Cosine formula
[tex]cos \theta = \frac{adj}{hyp}[/tex]
In this case:
[tex]cos \theta = \frac{y}{L}[/tex]
Multiply both sides by L
[tex]L * cos \theta = \frac{y}{L} * L[/tex]
[tex]Lcos \theta = y[/tex]
[tex]y = Lcos \theta[/tex]
[tex]y = Lcos75[/tex]
This can be used if the length (L) of the ladder is known.
Assume L = 15
[tex]y = 15 * cos75[/tex]
[tex]y = 3.88[/tex]
