Isaac DodunskiTrigonometry Project

24 June 2012

MethodThe aim of this investigation is to calculate the height of Mount Taranaki/Egmont, Paritutu Rock, and the New Plymouth Power Station chimney using a clinometer and trigonometry. The reason I chose these three objects is because they are tall Taranaki landmarks that everyone knows. I also wanted to use trigonometry with something as big as a mountain.

I made my clinometer by attaching a protractor to a plastic drinking straw. I then attached a piece of string with a weight on the end of it (see photo next page).

To get the readings I went to Ngamotu beach and used my clinometer to measure the angles to the top of Mount Taranaki, Paritutu Rock, and the New Plymouth Power Station chimney from sea level. While I looked through the straw my father would read the angle measured on the protractor part of the clinometer. We then wrote these angles down. To calculate the heights we needed to know the ground distance from Ngamotu Beach to the three landmarks. I got these measurements using Google map satellite images. The images came with the scale printed on the bottom left, and so I could calculate the distances from where I stood. The final step was using trigonometry (tan) to calculate the opposite side of the three right angle triangles. Two metres was added to every height calculation because this is roughly the distance from my eyes to the ground.

The final height calculations were surprisingly accurate for a home made clinometer. Because of the design, measurements could only be read to the nearest half degree. I could have read angles more accurately if the protractor was much larger. It was also hard to get an accurate measurement with the straw because of a bend in it. Another problem was that the weight kept moving around in the wind, which made it hard to get a reading that was spot on. The true heights are: Mount Taranaki – 2,518m, Paritutu Rock – 156m, and New Plymouth Power Station chimney – 198 metres.

One of the resources I used was Google maps to calculate the ground distances. The ground distances were used for the adjacent sides of the right angle triangles. My father showed me how to use the scales on Google maps to work out the distances. My father also assisted me with recording the angles from Ngamotu Beach because I wouldn’t have been able to look at the protractor readings at the same time as looking through the straw.

Equipment

Clinometer

Ngamotu Beach

Mount Taranaki

Paritutu Rock

NP Power Station Chimney