1) Find the answer: \(x \ = \ ?\)
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\(\color{red}{tan \ 45° \ = \ 1 \ = \ \frac{AB}{BC} \ = \ \frac{x}{7} \ ⇒ \ x \ = \ \frac{\sqrt{2}}{2} \times 7 \ = \ \frac{7\sqrt{2}}{2}}\)
2) Find the answer: \(x \ = \ ?\)
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\(\color{red}{tan \ x \ = \ \frac{AB}{BC} \ = \ \frac{5}{10} \ = \ \frac{1}{2} \ ⇒ \ x \ ≈ \ 26.565°}\)
3) Find the answer: \(x \ = \ ?\)
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\(\color{red}{tan \ 60° \ = \ \sqrt{3} \ = \ \frac{AB}{BC} \ = \ \frac{6}{x} \ ⇒ \ x \ = \ \frac{6}{\sqrt{3}} \ = \ 2\sqrt{3}}\)
4) Find the answer: \(x \ = \ ?\)
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\(\color{red}{tan \ 60° \ = \ \sqrt{3} \ = \ \frac{BC}{AB} \ = \ \frac{x}{11} \ ⇒ \ x \ = \ \sqrt{3} \times 11 \ = \ 11\sqrt{3}}\)
5) Find the answer: \(x \ = \ ?\)
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\(\color{red}{tan \ x \ = \ \frac{BC}{AB} \ = \ \frac{4\sqrt{3}}{4} \ = \ \sqrt{3} \ ⇒ \ x \ = \ 60°}\)
6) Find the answer: \(sin \ x \ = \ ? \ , \ cos \ x \ = \ ?\)
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\(\color{red}{AC \ = \ \sqrt{3^2 \ + \ 4^2} \ = \ 5}\)
\(\color{red}{sin \ x \ = \ \frac{BC}{AC} \ = \ \frac{4}{5}}\)
\(\color{red}{cos \ x \ = \ \frac{AB}{AC} \ = \ \frac{3}{5}}\)
7) Find the answer: \(cos \ x \ = \ ? \ , \ tan \ x \ = \ ?\)
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\(\color{red}{BC \ = \ \sqrt{10^2 \ - \ 8^2} \ = \ \sqrt{36} \ = \ 6}\)
\(\color{red}{cos \ x \ = \ \frac{BC}{AC} \ = \ \frac{6}{10} \ = \ \frac{3}{5}}\)
\(\color{red}{tan \ x \ = \ \frac{AB}{AC} \ = \ \frac{8}{6} \ = \ \frac{4}{3}}\)
8) Find the answer: \(cot \ x \ = \ ? \ , \ sin \ x \ = \ ?\)
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\(\color{red}{AB \ = \ \sqrt{15^2 \ - \ 12^2} \ = \ \sqrt{81} \ = \ 9}\)
\(\color{red}{cot \ x \ = \ \frac{BC}{AB} \ = \ \frac{12}{9} \ = \ \frac{4}{3}}\)
\(\color{red}{sin \ x \ = \ \frac{AB}{AC} \ = \ \frac{9}{15} \ = \ \frac{3}{5}}\)
9) Find the answer: \(x \ = \ ?\)
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\(\color{red}{cos \ 45° \ = \ \frac{\sqrt{2}}{2} \ = \ \frac{BC}{AC} \ = \ \frac{9}{x} \ ⇒ \ x \ = \ 9 \times \frac{2}{\sqrt{2}} \ = \ \frac{\sqrt{2}}{9}}\)
10) Find the answer: \(x \ = \ ?\)
.png)
\(\color{red}{cos \ 49° \ ≈ \ 0.656 \ = \ \frac{BC}{AC} \ = \ \frac{9}{x} \ ⇒ \ x \ = \ 9 \times \frac{1}{0.656} \ ≈ \ 13.719}\)
