SOLUTION: Kari has an analog clock, shown here, with a minute hand of length 12 in. When Kari’s clock strikes 2 o’clock, what is the area of the right triangle formed by drawing a segment fr

Algebra.Com
Question 457874: Kari has an analog clock, shown here, with a minute hand of length 12 in. When Kari’s clock strikes 2 o’clock, what is the area of the right triangle formed by drawing a segment from the end of the minute hand to the end of the hour hand? Express your answer in simplest radical form.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Kari has an analog clock, shown here, with a minute hand of length 12 in. When Kari’s clock strikes 2 o’clock, what is the area of the right triangle formed by drawing a segment from the end of the minute hand to the end of the hour hand? Express your answer in simplest radical form.
The angle between the hands at 2:00 is 2/12ths of 360°
or 1/6th of 360° or 60° 





Therefore the triangle is a 60°-30°-90° right triangle.  The hypotenuse
of such a right triangle is twice the shorter leg.  Therefore
the shorter leg is half of 12 in. or 6 in.

The green line is found by the Pythagorean theorem.

 c˛ = a˛ + b˛
12˛ = 6˛ + b˛
144 = 36 + b˛
108 = b˛
 b˛ = 108
       ___
  b = √108
       ____
  b = √36*3
        _
  b = 6√3


The formula for the area of a triangle is

   A = ˝(base)(height)
                     _
base = 6, height = 6√3
              _
   A = ˝(6)(6√3)
          _
   A = 18√3 square feet.

Edwin
RELATED QUESTIONS

Temi’s analog clock, shown here, has an hour hand of length 9 in and a minute hand of... (answered by jorel1380)
An analog clock shows 2:36 pm. What is the angle between the hour and minute... (answered by ikleyn,Boreal)
The minute hand of a clock is 6 inches long and moves from 3 o’clock to 5 o’clock. How... (answered by josmiceli)
A clock has hour and minute hands 1 and 1.6 inches long respectively. At what rate are... (answered by robertb,ikleyn)
The hour hand of a clock is 77.0 mm long. How far does the tip of the hand travel between (answered by ikleyn)
The minute hand of a clock in a clock tower has a length of 36 inches. If a butterfly... (answered by ikleyn)
John has two clocks: Clock A and Clock B. Clock A runs properly. Clock B, however, runs... (answered by stanbon)
The hour hand of a clock moves from 12 to 5 o’clock. Through how many degrees does it... (answered by Fombitz)
a clock strikes once at 1 o' clock, twice at 2 o' clock, three times at 3 o' clock, and... (answered by stanbon)