A mathematical and physical education teacher

Geometry Level pending

In a circle of radius 5 kilometers, Hector is at point B and he has to run to point A. His physical education teacher tolds him "i am 3.5 km away from the center of the circle, towards point B".

Hector must bet the time (in minutes) he will need to reach point A, knowing he runs at 14km /h.

How many minutes will he bet ? Give the response to 2 decimal places.

Enjoy


The answer is 16.87.

Dan Tsaranou by Dan Tsaranou , 21, France

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1 solution

Dan Tsaranou
Jan 10, 2016

First of all we need to know DA.

D A = 5 ² − 3.5 ² = 51 2 DA = \sqrt{5²-3.5²}= \frac {\sqrt{51}}{2} .

And so the angle BOA is cot ⁡ 3.5 D A \cot \frac{3.5}{DA} . We now can use propotionality: 10 π ∗ ∠ B O A 360 = 3.88 \frac {10π * \angle BOA}{ 360} = 3.88

AB is now equal to 3.88

The formula of speed is V = D T V= \frac {D}{T} so T = D V T= \frac {D}{V}

14 km/h = 0.23 km / min

T = 3.88 0.23 T = \frac{3.88}{0.23}

T = 16.87

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