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Notes

Problems

\(\textbf{1)}\) Solve for z.

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The answer is \( z=\sqrt{61} \approx7.81 \)

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\(\,\,\,\,\,\,a^2+b^2=c^2\)

\(\,\,\,\,\,\,5^2+6^2=z^2\)

\(\,\,\,\,\,\,25+36=z^2\)

\(\,\,\,\,\,\,61=z^2\)

\(\,\,\,\,\,\,\sqrt{61}=\sqrt{z^2}\)

\(\,\,\,\,\,\,\sqrt{61}=z\)

\(\,\,\,\,\,\,\text{The answer is } z=\sqrt{61} \approx7.81 \)

\(\textbf{2)}\) Solve for x.

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The answer is \( x=5 \)

\(\textbf{3)}\) Solve for y.

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The answer is \( y=\sqrt{91} \approx 9.54 \)

\(\textbf{4)}\) Solve for h.

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The answer is \(5 \)

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\(\,\,\,\,\,\,a^2+b^2=c^2\)

\(\,\,\,\,\,\,a^2+(12)^2=(13)^2\)

\(\,\,\,\,\,\,a^2+144=169\)

\(\,\,\,\,\,\,a^2=25\)

\(\,\,\,\,\,\,a=\sqrt{25}\)

\(\,\,\,\,\,\,a=5\)

\(\,\,\,\,\,\,\)The answer is \(5 \)

Challenge Problem

\(\textbf{5)}\) Two cars started at the same place. One car going north traveled 10 mph for 4 hours. The other car traveled east at 15 mph for 2 hours. How far apart are the cars?

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The answer is \(50 \) miles

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\(\bullet\text{ Special Right Triangles (30-60-90 and 45-45-90)}\)
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