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Alika [10]
2 years ago
7

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

Geography
1 answer:
Westkost [7]2 years ago
3 0

Answer:

<em>See explanation</em>

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.

<em>See attachment for illustration</em>

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

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