Greenwood press
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book-20600
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- TRIANGLE TRIGONOMETRY
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145 Transposition from C major to G major. Left: A translation pattern from Pueblo pottery. Right: A glide reflection— a translation alternated with a reflection. TRIANGLE TRIGONOMETRY Trigonometry can be used to find unknown lengths or angle measurements. In a situation involving right triangles, only a side length and an angle measure- ment are needed to determine the length of an object. This information is useful to engineers, because they can find large or hard-to-measure distances without having to measure them. For example, the height of a flagpole or a tall building can be determined using a measured distance from the pole and an angle of ele- vation from the ground (see below). Suppose you measure a distance 10 meters away from a flagpole along the ground. You record an angle of elevation at that point equal to 40°, as depicted. In right-triangle trigonometry, one of the following three ratios can be used to find the flag height of the poll: sin θ = opposite hypotenuse cos θ = adjacent hypotenuse tan θ = opposite adjacent . In this case, tan θ (pronounced tangent) should be used, because the opposite side from the angle of elevation θ is unknown (the height of the flagpole), and the adjacent side is the distance along the ground of 10 meters. Therefore the height of the flagpole, approximately 8.4 meters, can be found by solving the equation tan 40 ◦ = flagpole 10 . Sometimes the angle of elevation is recorded from an object above the ground, such as a transit sitting on a tripod, as illustrated. If the angle measurement is not taken from the ground, then the height of the tripod will need to be included in the final calculation. In this case, if the transit is 1.5 meters off of the ground, then the angle of elevation would be approximately 35° (see the following figure). The missing length will be approximately 6.9 meters, after setting up an equation using the tangent function, tan 35 ◦ = length above transit 10 . To find the complete flagpole length, the height of the transit will need to be added to this calculation in order to obtain the same answer calculated earlier. Download 1.81 Mb. Do'stlaringiz bilan baham: |
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