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3 years ago

The lengths of two sides of a right angled triangle are 20 cm and 30 cm.

Mathematics

1 answer:

Naddik [55]3 years ago

3 0

Answers:

Part (a) 10*sqrt(13)
Part (b) 10*sqrt(5)

Those values are exact. They approximate to:

10*sqrt(13) = 36.0555

10*sqrt(5) = 22.3607

====================================================

Explanation:

Part (a)

If the unknown third side is the hypotenuse then we need to find the value of c when a = 20 and b = 30.

Apply the pythagorean theorem

a^2 + b^2 = c^2

20^2 + 30^2 = c^2

400 + 900 = c^2

1300 = c^2

c^2 = 1300

c = sqrt(1300)

c = sqrt(100*13)

c = sqrt(100)*sqrt(13)

c = 10*sqrt(13) .... exact length

c = 36.0555 ...... approximate length

------------------------------------

Part (b)

If the third side is not the hypotenuse then that must mean c = 30 is the hypotenuse as this side is larger than the 20 cm side. The hypotenuse is always the longest side.

Let a = 20 be the known leg. Let's find the other unknown leg b using the pythagorean theorem.

a^2 + b^2 = c^2

20^2 + b^2 = 30^2

400 + b^2 = 900

b^2 = 900-400

b^2 = 500

b = sqrt(500)

b = sqrt(100*5)

b = sqrt(100)*sqrt(5)

b = 10*sqrt(5) ..... exact length

b = 22.3607 ....... approximate length

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A plane traveled 240 miles. The trip was with the wind. It took 3 hours. The trip back was into the wind. The trip back took 6 h

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Here we got our first equation for the second equation we use the information from the second trip which was into the wind. Which means the speed here would be speed=s-w

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$s+w=80\\60+w=80\\w=80-60\\w=20$

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