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.