Problem solving with trigonometry means using some of your own ideas to solve multistep or applied right angle triangle problems. It is about transferring your understanding of SOH CAH TOA and the Pythagorean theorem to any question that can be solved using this math.
Sometimes you need to use a combination of SOH CAH TOA math and some other math that you’ve already learned – for example, the area of a triangle.
The path to the solution is yours to create. However there are some problem solving approaches you can practice. Also, certain questions or types of question are more common than others.
Begin by drawing a diagram. Draw your diagram so that the angles look approximately correct. If you are drawing a right angle, make sure the angle on your drawing looks like a right angle.
For any question where you feel lost as to how to begin, you can get going by thinking about these questions:
- What information is given to me in the question?
- What information am I supposed to be able to calculate?
- Do I have any numerical values? If so, what ones?
- Do I have any algebraic values? If so, what do they represent?
- Am I going to end up with a number or with an algebraic expression?
- What numerical values do I wish I was told already?
- What labelling can I do on the diagram?
- What information do I already know how to calculate, even if it isn’t the answer I’m looking for?
Estimate the answer from the diagram to check your calculations are reasonable before looking at the answers given.
Here are some questions that math teachers/examiners often ask students to solve. The answers are given however the ‘step by step’ is left to you.
Solve the Triangle.
This question might appear challenging at first because you’re not told exactly what to do. You have to decide.
To ‘solve’ means to calculate all angles or sides that are not already given.
There are multiple correct approaches.
- Draw a diagram, choose one value to calculate first and call it
. Label the diagram accordingly and calculate its value. - Choose a second value to calculate, and call it
, calculate. - The last value, call it
and calculate it. - In this question, you can also draw on your knowledge that all the two acute angles in a right angled triangle add to 90 degrees.
More than Enough Information
In these problems, you are given more information than strictly required. That means that there is more than one correct way to approach the problem. One technique is to cover up one of the values given, which reduces the number of ways the question can be answered.
Isosceles Triangle
Calculate the height, the sides not shown and the angles not shown in these isosceles triangles.
A common method for solving problems is to introduce a dimension that is not drawn in the original diagram. When you draw a diagram of an isosceles triangle, draw on the line of symmetry. Think of the isosceles triangle as two right angled triangles.
Non-Right-Angled Triangle
to be continued…
Other Multi-Step Geometry Problems
to be continued…
Trees, Ladders, Planes, Flag poles
to be continued…
Problems with algebraic expressions
to be continued…
Right Angle Triangle Problem Set pdf
Solutions RA Triangle Problem Set pdf