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Math Help - Help With Special Right Triangles

  1. #1
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    Help With Special Right Triangles

    Here is my problem. I will send it in attachments but if you can't see the triangles in the attachment i will explain it.

    Fill in the missing side lengths and angle measures for each special right triangle below.

    Some of your answers will contain a square root () symbol.

    The 1st triangle is A 30-60-90 degree Triangle. the 30-60 Side Length is 8. But Whta Are The Others.

    The 2nd Triangle is A 40-40-90 degree Triangle. The 40-90 Side Length is 6. Wouldn't that make the other 40-90 side A 6 (Is This Right). So what is the missing side.

    Help. Please. I Will Be Very Grateful.
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  2. #2
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    Quote Originally Posted by dgenerationx2 View Post
    Here is my problem. I will send it in attachments but if you can't see the triangles in the attachment i will explain it.

    Fill in the missing side lengths and angle measures for each special right triangle below.

    Some of your answers will contain a square root () symbol.

    The 1st triangle is A 30-60-90 degree Triangle. the 30-60 Side Length is 8. But Whta Are The Others.

    The 2nd Triangle is A 40-40-90 degree Triangle. The 40-90 Side Length is 6. Wouldn't that make the other 40-90 side A 6 (Is This Right). So what is the missing side.

    Help. Please. I Will Be Very Grateful.
    You need to memorize a few rules about these types of triangles. And, by the way, I think you meant to say 45-45-90 in your 2nd triangle.

    For a 30-60-90 triangle, the hypotenuse is twice the short side (side opp. the 30 deg. angle) and the long side (side opp. 60 deg. angle) is equal to the short side times the square root of 3.

    You are given the hypotenuse = 8. The side opposite the 30 deg. angle would be 1/2 of 8 or 4. The side opp. the 60 deg. angle would be 4\sqrt{3}.

    In the 45-45-90 triangle, the two legs are equal and the hypotenuse is equal to a leg times the square root of 2.

    You are given a leg of 6. Therefore, the hypotenuse is 6\sqrt{2}

    These rules can easily be found using the Pathagorean theorem, but it's best if you just memorize them.
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