Discussion on: Plane Trigonometry

Submitted by Jaywelle T. Galagar on

Following is a discussion on the Reviewer item titled: Plane Trigonometry.
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Jaywelle T. Galagar Fri, 06/05/2015 - 21:03

a clock has a minute hand 16 cm long and an hour hand 11 cm long. find the distance between the outer tips of the hand at 2:30 o'clock?. . help me

joelitomath1971 Mon, 06/08/2015 - 21:23

After sketching a diagram for the problem, you will see that you are dealing with an oblique triangle. Let a=11 cm, b=16 cm, C=105 degrees. You are actually solving for c (the length of the third side of the triangle, which is also the distance between the outer tips of the hands of the clock).
You may now use the Law of Cosines to solve for c. Use the formula: c=a^2+b^2-2ab cos⁡C.
Substituting the values,c =〖(11)〗^2+〖(16)〗^2-2(11)(16) cos⁡〖〖105〗^o 〗. Please figure out what is the final answer. The final unit is in cm. Hope this helps... Good luck!

anmol agarwal Thu, 01/07/2016 - 19:43

Angle b/w the hands = 180-75=105°

Now looking to it as a triangle with 2 sides 16 and 11 cm and angle b/w them as 105°

By cosine formulae

Cos 105=(16^2+ 11^2-x^2)/(2*16*11)

(-0.259)=(377- x^2)/(352)

x^2=468.17

x=21.63

Hence solved

Hope its correct and understood