Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

A 45-45-90 triangle has a hypotenuse with a length of 10 ft. What are the lengths of the other legs?

What are the lengths of the other legs?

A)9.14 ft

B)7.07 ft

C)8.46 ft

D)6.36 ft

9 Answers

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  • 1 month ago
    Favorite Answer

    45-45-90 triangle is an isosceles triangle. Therefore, it will have 2 equal sides.

    Let the equal sides be xFor a right-angled triangle, by Pythagoras Theorem,x^2 + x^2 = 10^2

            2x^2 = 100

              x^2 = 50

                  x = 7.07       (since x > 0)

    The answer is B

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  • 1 month ago

    =sqrt((10*10)/2)=sqrt(50)=7.07 ft  B.

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  • Como
    Lv 7
    1 month ago

    x²  +  x²   =  10²

    2 x²   = 100

    x²   =  50

    x   = 5 √2

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  • 1 month ago

    Let x be the leg length.

    sin45 = x/10

    0.707 = x/10

    x = 7.07 ft

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  • David
    Lv 7
    1 month ago

    Using Pythagoras' theorem the other legs are 7.07 ft which is option B)

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  • RR
    Lv 7
    1 month ago

    It is an isosceles triangle. The base is the hypotenuse. The other sides will be equal to each other.

    Pythagoras:

    a^2 + b^2 = h^2

    a^2 + b^2 = 10^2

    but a = b, so substitute:

    b^2 + b^2 = 10^2

    2b^2 = 100

    b^2 = 50

    b = 7.07

    ANS (B)

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  • sepia
    Lv 7
    1 month ago

    A 45°–45°–90° triangle has a hypotenuse with a length of 10 ft.

    What are the lengths of the other legs? 

    n√2 = 10 feet

    n = 7.071067812 feet   

    Answer choice:

    B) 7.07 ft  

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  • 1 month ago

    There are a couple of ways to do this.

    The most basic way is to apply the Pythagorean Theorem.

    A-squared + B-squared = C-squared

    since A and B are the same in the triangle described

    2(A-squared) = C-squared

    2(A-squared) = 10 squared

    2(A-squared) = 100

    A-squared = 50

    A = sqrt(50)

    which

    I'd guess

    is answer B

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  • Pope
    Lv 7
    1 month ago

    You must want the legs, not the "other" legs, since the hypotenuse it not a leg.

    The lengths of the hypotenuse and a leg are in ratio √(2) : 1. It would be worth the effort to become familiar with this and the ratio of sides for a 30-60-90 triangle.

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