Question

When Carla solved for the height from the ground to the point where the ladder

Answer 1

Answer:

See explanation

Explanation:

Given

Represent the vertical angle with $\theta$

$\theta = 75$

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

$tan \theta = \frac{opp}{adj}$

In this case:

$tan \theta = \frac{x}{y}$

Multiply both sides by y

$y * tan \theta = \frac{x}{y} * y$

$y * tan \theta = x$

Divide both sides by tan

$y = \frac{x}{tan \theta}$

$y = \frac{x}{tan 75}$

This can be used if the distance (x) between the ladder and the wall is known.

Assume x = 15

$y = \frac{15}{tan 75}$

$y = 4.02$

2. Cosine formula

$cos \theta = \frac{adj}{hyp}$

In this case:

$cos \theta = \frac{y}{L}$

Multiply both sides by L

$L * cos \theta = \frac{y}{L} * L$

$Lcos \theta = y$

$y = Lcos \theta$

$y = Lcos75$

This can be used if the length (L) of the ladder is known.

Assume L = 15

$y = 15 * cos75$

$y = 3.88$