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Anna007 [38]
3 years ago
15

Solve the right triangle. Round decimal answer to the nearest 10th

Mathematics
1 answer:
kotegsom [21]3 years ago
6 0
Cos ∠A = adj/hyp 
∠A = cos⁻¹ (adj/hyp)
∠A = cos⁻¹ (10/15)
∠A = 48.2° (nearest tenth)

sin ∠B = opp/hyp
∠B = sin⁻¹ (opp/hyp)
∠B= sin⁻¹ (10/15)
∠B = 41.8°(nearest tenth)

a² + b² = c²
BC² + 10² = 15²
BC² = 15² - 10²
BC² = 125
BC = √125
BC = 11.2 units (nearest tenth)


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Explanation

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Step 1

multiplicate by the conjugate

\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}

notice that

\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\  \end{gathered}\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}

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Step-by-step explanation:

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