Let's suppose we need to find the height of a pole, but it is rather difficult on us to measure vertically let's consider the following alternative.
Problem: You are standing close to a pole. At the same time of the day you cast a shadow of x meter and the pole of y meters. We know your height to be h meters, find the height T of the pole.
Solution: Using proportions to solve the problem,
Calculate the height of a tree 24m away from Tom, given the area of 72m.
This method is usually given when the area and base is given...or......
You can also use the formula for solving the Area of a Triangle:
1/2 base*height....depending on the question
It is an interesting problem. You are in a plain ground and see a beautiful tall tree. You do not have any sophisticated instrument to find its height but are interested in finding it's height. What to do?
Take two straight poles one long and the other short. Fix the taller at about 20 feet from the tree vertically. Go further away from the tree in the same alignment so that on fixing the shorter vertically makes the tree top and the tops of the longer & shorter poles in a straight line. Measure the following:
Distance of longer pole from the tree, let it be L1
Distance of shorter pole from the longer pole, let it be L2
Height of longer pole above ground, let it be H1
Height of shorter pole above the ground, let it be H2
Let height of tree be Ht
Using ratio and proportion, we get
(Ht-H1)/(H1-H2) = L1/L2
Ht = (L1-L2)*(H1-H2) + H1
Height of Tree is (L1-L2)*(H1-H2) + H1
and height of tree can be so determined using ratios and proportions without using trigonometry.