Question

using the pythagorean theorem, calculate the value:1. right triangle with legs 9cm and 12cm, find the hypotenuse c2. right triangle with legs 15cm and 20cm, find the hypotenuse c3. right triangle with one leg 30cm, hypotenuse 78cm, find the other leg b4. right triangle with one leg 45cm, hypotenuse 51cm, find the other leg a5. right triangle with legs 32cm and 60cm, find the hypotenuse c

Explanation:

Step1: Apply Pythagoras theorem

For right triangles, $c^2=a^2+b^2$ or $a^2=c^2-b^2$
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Step2: Solve first triangle

$c=\sqrt{9^2+12^2}=\sqrt{81+144}=\sqrt{225}=15$

Step3: Solve second triangle

$c=\sqrt{15^2+20^2}=\sqrt{225+400}=\sqrt{625}=25$

Step4: Solve third triangle

$b=\sqrt{78^2-30^2}=\sqrt{6084-900}=\sqrt{5184}=72$

Step5: Solve fourth triangle

$a=\sqrt{51^2-45^2}=\sqrt{2601-2025}=\sqrt{576}=24$

Step6: Solve fifth triangle

$c=\sqrt{60^2+32^2}=\sqrt{3600+1024}=\sqrt{4624}=68$

Answer:

1. 15 cm
2. 25 cm
3. 72 cm
4. 24 cm
5. 68 cm