[You should have completed the trigonometry pages first]
The assignment was to find the height of the gym wall (outside) using trigonometry. This kind of calculation can be done by making just two measurements. We'll need the distance to the wall, and the angle of inclination of the top of the wall. Then we'll use a trig ratio to help calculate the wall's height.
The first step is to carefully measure the distance to the bottom of the wall from a selected location, using a tape measure.
We measured a distance of exactly 10 m.


The next step is to measure the angle of inclination to the top of the wall. This can be done using a device called a clinometer. We used several different types. A blackboard protractor, thumbtack, string and weight can be used to make a simple one if you don't have a real clinometer.
We did the angle measurement several times, and found an average value of 24 degrees.


Here is our diagram. Our measurements of 24° and 10 m are shown. When we drew the diagram, we realized we had a small problem. The measurements were taken above ground level, so our triangle is actually elevated by the height of the measuring instrument.
This means we will also have to measure that height, and add it to our final answer. We used two different devices; the calculation we are showing is for the clinometer on a stand; its height above the ground was 1.20 metres.

Here's the diagram of the triangle we'll be using to solve for x. The names of the sides are marked on the triangle.
Because we're using opposite and adjacent, the trig ratio needed will be opposite over adjacent, or tan.
If you forget the trig ratios, you can recall them using the acronym SOHCAHTOA.


Here is the calculation ...
Because all 24° right triangles are similar, the ratios of their sides are always the same. So your calculator can provide the value for what the tan24 ratio is supposed to be.
By rearranging and solving, you can determine the correct value for x to make the side ratio equal to tan24.


Now we need to add on the height of the measuring instrument (and the triangle) above the ground. That value was 1.20 m.
So the height of the gym works out to 5.65 m.


Mr. Willis' Page
