### So Big

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

### Gold Again

Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.

### Bend

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?

# 30-60-90 Polypuzzle

##### Stage: 5 Challenge Level:

Finding the lengths depends on using the ratio for the sides of a 30-60-90 triangle as the name of the problem suggests. Below the diagrams show how to take the pieces which make a square of unit area and fit the pieces together to make an equilateral triangle of the same area with side $2t$ and knowing this you can calculate $t$. The way pieces fit together gives you that $p=t$ and the rest is up to you!

You can calculate the length '$t$' knowing the area of the equilateral triangle. Pythagoras theorem and the sine rule can be used in finding the other lengths.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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