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Draw and label a diagram, then use the trigonometric ratios to solve the following problems. Label the units. Part 1. Show the work.

1. Hudson uses scissors to cut a rectangular piece of paper from one corner to the opposite corner. The cut is 24 centimeters long, and makes a 55 with the uncut edge. How many centimeters long is the paper?


2. Jamar is using a treadmill. He sets the 48 inch at an incline of 10 degree, how high is the end of the treadmill raised?


3. Find the angle of elevation of the sun when a 12.5 meter tall telephone pole casts an 18 meter long shadow.

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sqdancefan

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Answer:

  1. 19.7 cm
  2. 8.3 in
  3. 34.8°

Step-by-step explanation:

1. The longer side of the paper is opposite the 55° angle, so the sine function is applicable.

  s = (24 cm)sin(55°) ≈ 19.7 cm

The paper is about 19.7 cm long.

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2. (The treadmill picture is substantially identical to the paper/scissors picture. The length is 48 in instead of 24 cm, and the angle is 10° instead of 55°.)

The height is measured opposite the angle, so the sine function applies.

  h = 48·sin(10°) ≈ 8.34

The end of the treadmill is raised about 8.3 inches.

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3. The given measurements are of sides adjacent and opposite the angle being measured, so the tangent function applies.

  tan(angle) = (12.5 m)/(18 m)

  angle = arctan(25/36) ≈ 34.78°

The angle of elevation of the sun is about 34.8°.

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