Question

Use the diagram attached below. Find the straight distance between the zoo and movie theater.

This is greatly appreciated. Thank you :)

Answer 1

The distance would be around 9.66 blocks

Explanation:

If you draw a straight line from zoo to movie theater, we have a triangle.

The given angle is 86 degrees, the two sides adjacent to it are 6 and 8 and we want to find the side opposite (let it be "p") to the given angle.

We will use cosine rule to find this. The rule is:

`p^2=a^2+b^2-2abcosP`

Where

a and b are the two adjacent sides to the given angle

a = 6

b = 8

p is what we are looking for

P is the angle given

So, substituting and finding the value:

`p^2=a^2+b^2-2abcosP\\p^2=6^2 + 8^2 - 2(6)(8)Cos(86)\\p^2=36+64-96Cos(86)\\p^2=100-96Cos(86)\\p^2=93.3033\\p=√(93.3033)\\p=9.66`

The distance would be around 9.66 blocks