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nikitadnepr [17]
2 years ago
15

Analyze the diagram below and complete the instructions that follow. Find a, b, and c.

Mathematics
1 answer:
ahrayia [7]2 years ago
5 0

Answer:

<u>The correct answer is the letter C. </u>

Step-by-step explanation:

We can use the following trigonometric identity:

cos(60)=\frac{6}{b} (1)

cos(45)=\frac{c}{b} (2)

Solving each equation by b and equaling we have:

\frac{6}{cos(60)}=\frac{c}{cos(45)}

\frac{6}{cos(60)}=\frac{c}{cos(45)}

Let's recall that:

cos(45)=\frac{1}{\sqrt{2}}

cos(60)=\frac{1}{2}

Then we have:

c=\frac{cos(45)*6}{cos(60)}

c=\frac{2*6}{\sqrt{2}}

c=\frac{12}{\sqrt{2}}

c=6\sqrt{2}

Using equation (1) we can find b.

cos(60)=\frac{6}{b}  

b=12      

Finally, we can find a using the next equation:

tan(60)=\frac{a}{6}

a=6*tan(60)

a=6\sqrt{3}

<u>Therefore, the correct answer is the letter C. </u>

I hope it helps you!

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