Problem Solving Angles

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OK, now that you've saved the airplane from crashing, you decide to retire and use your geometry skills in a cushy job building ski lifts for rich tourists in Switzerland. Ski Lift Corp wants to build a ski lift at a 30-degree angle of elevation up to the very peak of a mountain.You'll also learn how to solve problems related to angles of elevation and depression using basic trigonometric relationships Quick!What do crashing airplanes, ski lifts, and looking at people from the top of a hill all have in common?We can now use basic trigonometric relationships to solve for x and y because thanks to the TOA in SOH-CAH-TOA, we know that the tangent of 30 must equal the opposite side over the adjacent side, so tan(30) = 10,000/y.If we solve this, we find that y = approximately 17,331 feet, which is roughly 3.3 miles.Trigonometry's connection to measurement places it in the learner's manuals for a wide variety of professions.Carpenters, construction workers, designers, architects, and engineers, to name a few, deal with measurements, and as such, they deal with triangle measures, or trigonometry.• It is assumed that the tower is vertical, making it perpendicular with the ground.• This solution will use alternate interior angles from the parallel horizontal lines, so place 40º inside the triangle by the partner (bottom right).The answer: you can make mathematical models of all of them with angles of elevation and depression!If a person is standing on the ground, looking up at something in the sky, the angle of elevation is the angle formed between the person's line of sight and the ground.


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