Greenwood press
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book-20600
146
TRIANGLE TRIGONOMETRY The height of a tall object, such as a flagpole, can be determined with trigonometry by measuring a distance along the ground and an angle of elevation. Engineers use transits to measure angles of tall or hard-to-reach objects. Right-triangle trigonometry can be used to determine an unknown angle based on two lengths. For example, the navigator of a ship will try to minimize the traveling distance by adjusting the direction of the boat to account for the water’s current. If the current is moving parallel to the waterfront, then the speed of the boat observed from land will be greater due to the push from the current. Suppose that the ship is moving perpendicular to the shore at 40 feet per second and is recording a land speed of 42 feet per second. The current will push the boat off course if it is trying to reach a destination directly across the river. Using the cosine of the angle cos θ, the ship’s navigator can determine the angle in which to rotate the boat so that it does not move off course. The cosine function is used in this case, because the two measurements known are the adjacent (the boat speed) and hypotenuse (the land speed) sides of the right triangle. Substituting the given values in this relationship, the unknown angle of 17.8° can be found by solving the equation cos θ = 40 42 . To find an angle measurement, the inverse cosine of the ratio, or cos −1 (40/42), needs to be entered on the calculator. This means that if the boat moves straight towards its journey, it will actually veer off course by 17.8°. If the boat is still headed straight without accounting for the current, it will veer almost one-third of a mile off course for every mile traveled. To avoid this problem, the ship’s navigator will have to turn the boat 17.8° away from the perpendicular path and against the cur- rent in order to travel directly across the river. Applications of right-triangle trigonometry also exist in areas outside of sur- veying and navigation. Air-traffic control at small airports must establish the cloud height in the evening to determine if there is enough visibility for pilots to safely land their planes. A light source directed at a constant angle of 70° towards the clouds situated 1,000 feet from an observer, and the observer’s angle of ele- Download 1.81 Mb. Do'stlaringiz bilan baham: |
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