 
On this page we'll practice solving a small selection of some common grade 10 trigonometry problems that you've seen in class. You might first want to review basic trig operations. You can also review common terms and measuring devices. We will assume that all answers are to be rounded to one decimal place (lengths) or the nearest whole value (angles). Problem 1: 'You are on the ground 35 metres from the base of a tall tree. You measure the angle of inclination to the top of the tree to be 40 degrees. How tall is the tree?' In this first problem, since we are given no information about the height of the clinometer (angle-measuring device) used, we will assume the angle of inclination to the top of the tree is measured from ground level. Remember that the angle is measured where you are. Here's the diagram: 
Here is the diagram with only the essential information, including the side labels: 
You know how to use trigonometry to solve triangles, so we'll just show the solution:
Problem 2: 'You are on top of a 60 metre tall hill, Looking down at an armoured vehicle out on the field below. You measure its angle of declination to be 19 degrees. How far is the vehicle from you?' Once again, since we are given no information about the height of the clinometer above your feet, we will assume the angle of declination to the vehicle is measured from ground level at the top of the hill. Remember that the angle is measured where you are. In this case, it's an angle of declination, which means 'looking from the horizon downwards. Here's the diagram: 
Here is the diagram with only the essential information, including the side labels: 
You know how to solve triangles, and solving the resultant equation should be familiar, so we'll just show the solution:
If you had trouble understanding how we did the solving above, here is the solution with all the steps and explanations: 
Let's look at some more problems on page two ... |