Problem Solving Unit

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Year 10 Interactive Maths - Second Edition

Problem Solving Unit

Problem 15.1 Coins

You are given one coin with a diameter of 7 cm and a large supply of coins each with a diameter of 3 cm.

b. What is the maximum number of smaller coins that may be arranged tangentially around the
larger coin without any overlap?

Problem 15.2 Inscribed Triangle

A triangle is inscribed in a circle such that one side of the triangle is a diameter of the circle. If one of the acute angles of the triangle has measure 40º and the side adjacent to that angle has length 9 cm, find the radius of the circle.

Problem 15.3 Motorcycle Ramp

A slope of a motorcycle ramp is defined as the ratio (or comparison) between the vertical rise and the horizontal run when riding between two points on the ramp. That is:

1c. What angle to the nearest minute is made by a ramp of maximum allowable slope?

2a. Find the distance that the rider will cover on the following ramp (i.e. calculate BE).

2c. The rider moves at a constant speed of 30 km/h on the ramp. How long is he on the ramp for? Round your answer to the nearest second.

2d. Calculate the length of the diagonal AE.

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