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Use the Theorem of Pythagoras to show how you would find the hypotenuse in each of the following right-angled triangles.

Mathematics

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Answers

3 parts
a

p2+q2\sqrt{p^2 + q^2}

b

s2+t2\sqrt{s^2 + t^2}

c

o2+n2\sqrt{o^2 + n^2}

Step-by-step solution

6 steps

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs). If the legs are aa and bb, and the hypotenuse is cc, then a2+b2=c2a^2 + b^2 = c^2. To find the hypotenuse, we take the square root: c=a2+b2c = \sqrt{a^2 + b^2}.

Part a· 2 steps

  1. Identify the legs and the hypotenuse.

    The legs are pp and qq. The hypotenuse is rr.

  2. Apply the Pythagorean theorem to find the hypotenuse rr.

    r2=p2+q2r^2 = p^2 + q^2 r=p2+q2r = \boxed{\sqrt{p^2 + q^2}}

Part b

s2+t2\sqrt{s^2 + t^2}

  1. Identify the legs and the hypotenuse.

    The legs are ss and tt. The hypotenuse is uu.

  2. Apply the Pythagorean theorem to find the hypotenuse uu.

    u2=s2+t2u^2 = s^2 + t^2 u=s2+t2u = \boxed{\sqrt{s^2 + t^2}}

Part c

o2+n2\sqrt{o^2 + n^2}

  1. Identify the legs and the hypotenuse.

    The legs are oo and nn. The hypotenuse is mm.

  2. Apply the Pythagorean theorem to find the hypotenuse mm.

    m2=o2+n2m^2 = o^2 + n^2 m=o2+n2m = \boxed{\sqrt{o^2 + n^2}}
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