Trigonometry makes measuring nature easier.
Right angle trigonometry relies on the geometric ratios between sides and angles in right triangles to calculate the value of one part when the other is known--for instance, finding a missing angle when the sides are known. It can be extended and applied to many fields, including environmental science, geology and navigation. Using sine, tangent, cosine, a calculator, a ruler and a protractor, you can engage in many scientific activities to explore right angle trigonometry.
Approximating Tree Height
Because of the time and labor involved in measuring a tree from top to bottom, many researchers use trigonometry to accurately estimate tree heights. To do this, first, measure your distance, perhaps with a tape measure, from where you will be standing to the tree you are measuring. The units do not matter. Next, using a clinometer, measure the angle from your face to the top of the tree. If you do not have a clinometer, you can use a protractor with a free-weight attached to its center. As you angle the protractor in accordance to your line of vision to the top of the tree, the weight will create the "angle of elevation" of your eye sight to the tree top. Finally, use a calculator to determine the height of the tree. Since tangent of the angle, or tan(angle), = (opposite side)/(adjacent side), your tree height will equal (your distance from the tree) x [tan(angle)] + the distance from the ground to your eye level. For example, if you are 14 ft. from the tree, the tip of the tree is 55º from your eye level 5 ft. off the ground, then the tree height is 25.0 ft. [14 x tan(55º) + 5].
Measuring Width of a Stream
Start by measuring your distance directly across from some object on the other side of the stream, like a large rock or tree, to a point some distance along the stream but further down. From this new point, estimate the angle made from your starting position to your current position to the object on the other side of the stream. The best way to do this is with a compass. Approximate the degree of change in your compass from facing your starting position to facing the object on the other side of the stream. Even if your measurement is imprecise, you will be able to closely approximate the width of the stream using this information. For example, if your distance from the object directly across from you to further down the stream is 15 ft. and your compass changes by about 30º, then the stream width is 8.66 ft. [15 x tan(30º)].
Measuring the Sun's Angle of Elevation from the Earth
Throughout the day, the sun changes its position in the sky. The higher up it is, the shorter the shadow cast by objects of a given height. You can use this information to estimate the sun's angle to the Earth and the approximate heights of objects given their shadow length. Begin by taking a yardstick or any type of vertical, medium-sized object. Measure the height of the object. Then stand the object vertically in a place with no shade, and measure the shadow cast from the base of the object. For instance, if your 4 in. cell phone has a 3 in. shadow, then the sun's angle is 53.1º [tan ̄ ¹ (height/shadow) = tan ̄ ¹ (4/3)]. Therefore, if you know the shadow of a house is 8 ft. when the sun's angle is 53.1º, then its height is 10.7 ft. [8 x tan(53.1º)]. As the sun rises, its angle of elevation grows and shadow length correspondingly shrinks.
Tags: your distance, distance from, from your, object other, object other side, other side
