8 yd2 ydWhat is the length of the hypotenuse? If necessary, round to the nearest tenth.

8 yd
2 yd
What is the length of the hypotenuse? If necessary, round to the nearest tenth.


[tex]8 yd 2 yd What is the length of the hypotenuse? If necessary, round to the nearest tenth.[/tex]

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  1. [tex]\boxed {\boxed {\sf c \approx 2.2 \ inches}}[/tex]

    Step-by-step explanation:

    This triangle has a small square in the corner, representing a right angle. This means we can use the Pythagorean Theorem.

    [tex]a^2+b^2=c^2[/tex]

    Where a and b are the legs and c is the hypotenuse.

    In this triangle, the legs are 2 and 1, because they form the right angle. The hypotenuse, which is opposite the right angle, is unknown.

    a = 2b=1

    Substitute the known values into the formula.

    [tex](2)^2+(1)^2=c^2[/tex]

    Solve the exponents.

    (2)²= 2*2=4

    [tex]4+(1)^2=c^2[/tex]

    (1)²=1*1=1

    [tex]4+1=c^2[/tex]

    Add.

    [tex]5=c^2[/tex]

    Since we are solving for c, we must isolate the variable. Since it is being squared, we take the square root of both sides.

    [tex]\sqrt {5}= \sqrt{c^2} \\[/tex]

    [tex]2.2360679775=c[/tex]

    We have to round to the nearest tenth. The 3 in the hundredth place tells us to leave the 2 in the tenths place.

    [tex]2.2 \approx c[/tex]

    The hypotenuse is approximately 2.2 inches.

  2. 7.) Hypotenuse is 10

    8.)Hypotenuse is 10.3

    9.) Hypotenuse is 10.8

    10.) Hypotenuse is 9.1

    11.) Hypotenuse is 7.8

    12.) Hypotenuse is 2.7

  3. Step-by-step explanation:

    By Pythagoras' Theorem, a² + b² = c².

    Substituting the values of a and b, we get:

    7² + 25² = c²

    49 + 625 = c²

    c² = 674

    c ≈ 26.0 (to 1 d.p.)

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