Mathematics

Question

What is the length of the hypotenuse in the 30-60-90 triangle shown below ?

1 Answer

  • Answer:

    [tex]Hypotenuse=10[/tex]

    Step-by-step explanation:

    The missing figure is attached.

    For this exercise you can use the following Trigonometric Identity:

    [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]

    Let be "x" the hypotenuse of this right triangle.

    You can identify from the figure that, in this case:

    [tex]\alpha=60\°\\\\opposite=5\sqrt{3}[/tex]

    Then, knowing these values you can substitute them into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:

    [tex]sin(60\°)=\frac{5\sqrt{3}}{x}[/tex]

    Finally, you need to solve for "x" in order to find the lenght of the hypotenuse.

    This is:

    [tex]x*sin(60\°)=5\sqrt{3}\\\\x=\frac{5\sqrt{3}}{sin(60\°)}\\\\x=10[/tex]

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