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:
Without using a calculator, computer or tables find the exact
values of cos36cos72 and also cos36 - cos72.
What is the longest stick that can be carried horizontally along a
narrow corridor and around a right-angled bend?
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.