Question
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ITEM 3
Your father has a triangular piece of land that measures 8 cm long,
and one of the sides is 6 cm . The angle between two sides is .
Your father wants to construct a circular fence around histriangular
piece of land but does not know how to do it.
Task
As a student of S .1 , help your father to construct a circle through
the vertices of the triangularpiece of land.
ii. Work out the area of the circle (taking )
iii. If your father gives you his bank A.T.M to withdraw for him
the money to buy the construction materials and He gives the pin
as 179 in decimal base, what do you think will bethe four-digit pin
number in base five will you use to withdraw the money?

Ask by Ford Reeves. in Uganda
Dec 19,2024

Upstudy AI Solution

Tutor-Verified Answer

Answer

To help your father construct a circular fence around his triangular land:
  1. Calculate the third side of the triangle using the Law of Cosines.
  2. Find the area of the triangle using the formula for two sides and the included angle.
  3. Determine the circumradius ® of the triangle.
  4. Calculate the area of the circumcircle using .
Area of the circumcircle ≈ 53 cm².
For the PIN conversion:
  • Convert 179 from decimal to base five: 179 in decimal is 1204 in base five.
  • Four-digit PIN in base five: 1204.
So, the four-digit PIN in base five is 1204.

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Extra Insights

To help your father construct a circle around his triangular piece of land, you need to find the circumradius ® of the triangle formed. First, calculate the third side using the Law of Cosines: , where cm, cm, and . You would find cm. Once you have all three sides, the circumradius can be calculated using the formula , where is the area of the triangle found using Heron’s formula.
Next, for the area of the circle, use the formula . Assuming was calculated as around cm after working through the numbers, would be approximately cm² (using ).
Now, onto the pin conversion! To convert the decimal pin ‘179’ to base five, you keep dividing by 5, noting the remainders. When you do the conversions, you’ll find that the four-digit pin is in base five. Happy withdrawing!

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