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Curriculum: Georgia Performance Standards Topic: Right Triangles and Trigonometry Lesson: 29: Angles of Elevation and Depression
Attempt following question by selecting a choice to answer.
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The angle of elevation of the top of a dowel from a point on the ground is 54°. After walking 18 ft towards the dowel, the angle of elevation becomes 67°. What is the height of the dowel rounded to the nearest foot? c DA. D62 ft B. D64 ft C. D58 ft D. D60 ft
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Step 2: Draw the figure from the given data.  Step 3: Let P and Q be the points of observation and y be the height of the dowel. Step 4: In right triangle QRS, tan 67° = yxStep 5: x = ytan 67° » 0.424 y[Substitute the value of tan 67°.] [Use calculator.] Step 6: In right triangle PRS, tan 54° = y(18 + x)Step 7: 18 + x = ytan 54°[Substitute the value of tan 54° and simplify.] Step 8: 18 + x = 0.726 yStep 9: 18 + 0.424 y = 0.726 y[Substitute the value of x = 0.424 y.] Step 10: 18 = 0.302 yStep 11: y » 60 Step 12: Therefore, the height of the dowel is 60 ft.
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