El horario y el minutero de un reloj miden respectivamente 0.7 y 1.2cm. Determinar la distancia entre los extremos de dichas man

Question

4 years ago

11

ecillas a las 13:30 horas

1 answer:

Fed [463] · Answer 1 · 2021-12-25T12:14:24+03:00

Answer:

1.5887 cm

Step-by-step explanation:

If the time is 13:30, The hour pointer will be between the numbers 1 and 2.

Each number of the 12 number clock is separated by 30 degrees, so the hour pointer is at 45 degrees.

The minute pointer is at 30 minutes, so it is in number 6, being therefore at angle 180.

The angle formed by the pointers will be 180 - 45 = 135 degrees.

We can draw a triangle with both pointers and this angle (image attached)

So, we can calculate the distance between the tip of the pointers (let's call it "d") using law of cosines:

d^2 = 0.7^2 + 1.2^2 - 0.7*1.2*cos(135)

d^2 = 0.49 + 1.44 - (-0.5940) = 2.524

d = 1.5887 cm