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Math Help - Triangle

  1. #1
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    Triangle

    I have no idea how to do this...

    *An isosceles triangle has two sides that are 10cm long and a base that is 15cm long. If the angle between the congruent sides is 82degrees, what is the height of the triangle?
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  2. #2
    Junior Member JoanF's Avatar
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    Quote Originally Posted by ~NeonFire372~ View Post
    I have no idea how to do this...

    *An isosceles triangle has two sides that are 10cm long and a base that is 15cm long. If the angle between the congruent sides is 82degrees, what is the height of the triangle?
    Divide de triangle and use trigonometry: 82/2 = 41

    the hypotenuse of the new triangle is 10, so you can we trigonometry here or Pythagoras' theorem because you know that the base of the new triangle is 15/2=7,5 cm
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by ~NeonFire372~ View Post
    I have no idea how to do this...

    *An isosceles triangle has two sides that are 10cm long and a base that is 15cm long. If the angle between the congruent sides is 82degrees, what is the height of the triangle?
    Bisect the 82 degree angle so that it crosses the base in the exact middle. This means the new angle is 41 degrees and your half triangle has half the base. You can use pythagoras or trig to find the perpendicular height

    h = \sqrt{7.5^2+10^2}
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  4. #4
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    Quote Originally Posted by ~NeonFire372~ View Post
    I have no idea how to do this...

    *An isosceles triangle has two sides that are 10cm long and a base that is 15cm long. If the angle between the congruent sides is 82degrees, what is the height of the triangle?
    Since you have one angle and you know that the triangle is isosceles (meaning the other two angles will be equal to each other), we can figure out that the other two angles are both 49 (180 - 82 = 98. 98 divided by 2 = 49).

    This is what you should be looking at now:


    (Kind of messy, but you get the idea, haha.)

    The line down the middle is the Height (represented by h). The distance from the bottom to the top - that's what you have to find.

    Also, note that the base is 15. That means that both halves have a base of 7.5.

    Since we have all our angles and measures now, we can easily find the h by working one side of the split triangle. Turn it into a triangle of its own:



    It has a right angle, 90, and its B angle of 49. This means that the A angle is now 41.

    Now we can use the formula a^2 + b^2 = c^2 to get h.

    10^2 + 7.5^2 = h^2.

    156.25 = h^2.

    h = 12.5. And that's your answer.
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  5. #5
    Junior Member JoanF's Avatar
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    e^(i*pi) and Frontier , why did you put 10^2 + 7.5^2 = h^2??
    10 is the hypotenuse, I didn't understand
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  6. #6
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by JoanF View Post
    e^(i*pi) and Frontier , why did you put 10^2 + 7.5^2 = h^2??
    10 is the hypotenuse, I didn't understand
    Because I'm a citrus fruit and didn't spot that >.<

    The final side should be h = \sqrt{10^2-7.5^2}
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