Question

Can anyone explain how to do this? The answer isn't as important as the explanation. My teacher gave us a video w/o an example like this so I don't know what to do lol

Answer 1

x = 182.53

Explanation:

Use trigonometric ratios to find the whole side length (a) adjacent to 20° and the side length (b) adjacent to 57° respectively. Then find the difference. That would give you the value of x. That is: a - b = x

Let's solve.

✍️Finding the whole side length adjacent to 20°:

Opp = 87

Adjacent length = ? = a

`\theta = 20`

Thus,

`tan(\theta) = (opposite)/(adjacent)`

Plug in the values

`tan(20) = (87)/(a)`

Multiply both sides by a

`tan(20) * a = (87)/(a) * a`

`tan(20) * a = 87`

Divide both sides by tan(20)

`(tan(20) * a)/(tan(20)) = (87)/(tan(20))`

`a = (87)/(tan(20))`

`a = 239.03`

Finding the side length adjacent to 57°:

Opp = 87

Adjacent length = ? = b

`\theta = 57`

Thus,

`tan(\theta) = (opposite)/(adjacent)`

Plug in the values

`tan(57) = (87)/(b)`

Multiply both sides by b

`tan(57) * b = (87)/(b) * b`

`tan(57) * b = 87`

Divide both sides by tan(57)

`(tan(57) * b)/(tan(57)) = (87)/(tan(57))`

`b = (87)/(tan(57))`

`b = 56.50`

Therefore:

x = a - b

x = 239.03 - 56.50

x = 182.53