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2 years ago

Given: m space measured angle space C space equals space 76, a = 20, and b = 13. What is the length of c to the nearest tenth?

Mathematics

1 answer:

Komok [63]2 years ago

5 0

Based on the given parameters, the length of c is 8.0 units

<h3>How to determine the side length of c?</h3>

The given parameters are

Angle c = 76 degrees

Side a = 20

Side b = 13

The length of c is then calculated using the following law of sines

c^2 = a^2 + b^2 - 2absin(C)

Substitute the known values in the above equation

So, we have

c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)

Express 20^2 as 400

c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)

Express 13^2 as 169

c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)

Evaluate the product and sin(76)

c^2 = 400 + 169 - 520 * 0.9703

Evaluate the product

c^2 = 400 + 169 - 504.55

Evaluate the exponents

c^2 = 400 + 169 - 504.55

So, we have

c^2 = 64.45

Evaluate the square root

c = 8.0

Hence, the length of c is 8.0 units

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So we have the system of equations:
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Solving for $x$ in equation (2):
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Replacing equation (3) in equation (1):
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$y= \frac{7}{ \frac{10}{3} }$
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Replacing equation (4) in equation (3):
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