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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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Using the right-angled triangle pictured below (not to scale), find the specified side lengths or angles using trigonometry and the given values.

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Before starting, check that your calculator is in degrees mode by verifying that $\\cos{60} = \\dfrac{1}{2}$.

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(If your calculator does not give this answer, press SHIFT $\\rightarrow$ SETUP $\\rightarrow$ 3 to enter degrees mode if using a Casio $fx$ model calculator, otherwise refer to your calculator's manual.)

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$a=\\var{a[0]}$

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$x=\\var{x[0]}^\\circ$

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$c=$ [[0]]

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$b=\\var{a[1]}$

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$y=\\var{x[1]}^\\circ$

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$c=$ [[0]]

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$a=\\var{a[2]}$

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$y=\\var{x[2]}^\\circ$

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$c=$ [[0]]

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$b=\\var{a[3]}$

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$x=\\var{x[3]}^\\circ$

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$a=$ [[0]]

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$b=\\var{a[4]}$

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$x=\\var{x[4]}^\\circ$

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$c=$ [[0]]

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$a=\\var{fh}$

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$c=\\var{fa}$

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$x=$ [[0]]$^\\circ$

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$b=\\var{fa_1}$

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$c=\\var{fa}$

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$x=$ [[0]]$^\\circ$

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