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Math Help - trig functions

  1. #1
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    Question trig functions

    I am working on a project, and I was wondering if you could find a length of a side of a right triangle by using the trig functions such as

    sin A= opposite/hypotenuse, cos A=adjacent/hypotenuse, and
    tan A= opposite/adjacent

    (I know you can use pythagoreans theorem, but I need to find another way to find the missing side)

    If my example is
    Town x is 9 miles from town y, and 12 miles from town z. A road connects towns y and z directly. Find the length of this road. 9^2 + 12^2 = c^2

    how can i find the length of c using trig. functions? (I know c=15 by using pythagorean theorem)

    Please Help

    Thanks
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by mandy123 View Post
    I am working on a project, and I was wondering if you could find a length of a side of a right triangle by using the trig functions such as

    sin A= opposite/hypotenuse, cos A=adjacent/hypotenuse, and
    tan A= opposite/adjacent

    (I know you can use pythagoreans theorem, but I need to find another way to find the missing side)

    If my example is
    Town x is 9 miles from town y, and 12 miles from town z. A road connects towns y and z directly. Find the length of this road. 9^2 + 12^2 = c^2

    how can i find the length of c using trig. functions? (I know c=15 by using pythagorean theorem)

    Please Help

    Thanks
    Hi Mandy123,

    One must assume that the angle formed at town X to the other two towns is a right angle in order for your solution to work.

    One way using trig:

    \tan y=\frac{12}{9}

    y=\tan^{-1}\left(\frac{12}{9}\right)=53.13010235^{\circ}

    \sin (53.13010235^{\circ})=\frac{12}{c}

    c=\frac{12}{\sin (53.13010235^{\circ})}=15
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  3. #3
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    Thank you so much, i was missing the tangent inverse part, and my calculator was in the wrong mode, so thank you so much!!!!
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