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gizmo_the_mogwai [7]
3 years ago
9

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 l

ike this so I don't know what to do lol

Mathematics
1 answer:
solong [7]3 years ago
4 0

Answer:

x = 182.53

Step-by-step 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) = \frac{opposite}{adjacent}

Plug in the values

tan(20) = \frac{87}{a}

Multiply both sides by a

tan(20) \times a = \frac{87}{a} \times a

tan(20) \times a = 87

Divide both sides by tan(20)

\frac{tan(20) \times a}{tan(20)} = \frac{87}{tan(20)}

a = \frac{87}{tan(20)}

a = 239.03

Finding the side length adjacent to 57°:

Opp = 87

Adjacent length = ? = b

\theta = 57

Thus,

tan(\theta) = \frac{opposite}{adjacent}

Plug in the values

tan(57) = \frac{87}{b}

Multiply both sides by b

tan(57) \times b = \frac{87}{b} \times b

tan(57) \times b = 87

Divide both sides by tan(57)

\frac{tan(57) \times b}{tan(57)} = \frac{87}{tan(57)}

b = \frac{87}{tan(57)}

b = 56.50

Therefore:

x = a - b

x = 239.03 - 56.50

x = 182.53

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