Mathematics

Question

A right angle triangle is shown with hypotenuse equal to 13 centimeters. An acute angle of the triangle is labeled as x degrees. The side adjacent to the acute angle has length 5 centimeters and the side opposite to the acute angle has length 12 centimeters.

What is the value of sin x°?

2 Answer

  • sin = opposite/hypotenuse

    so sin (x) = 12/13

    answer is 12/13
  • Answer:

    the right answer is 12/13= 0.92

    Step-by-step explanation:

    with the data given we have:

    with the picture, we already have an idea of the data, and the question asks us to find the sin of x, remembering [tex]sin=[/tex] [tex]\frac{opposite}{hypotenuse}[/tex]

    so we need to find the value of the opposite

    Using the Pythagoras theorem [tex]opposite^{2}[/tex]+[tex]adjacent^{2}[/tex]= [tex]hypotenuse^{2}[/tex]

    rewriting

    [tex]opposite^{2}[/tex]=[tex]hypotenuse^{2}[/tex]-[tex]adjacent^{2}[/tex]

    opposite= [tex]\sqrt{hypotenuse^{2}-adjacent^{2}}[/tex]

    replacing we have

    opposyte= [tex]\sqrt({13^{2} }- 5^{2})[/tex]

    opposyte=[tex]\sqrt{169-25}[/tex]

    opposyte= [tex]\sqrt{144}[/tex]

    opposyte= 12

    now replaced in the formula of sin we have

    [tex]sinx=[/tex][tex]\frac{opposite}{hypotenuse}[/tex]  

    sinx=12/13

    sinx=0.92

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