Prentice Hall Geometry

See Problems 4 and 5.

Algebra Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

  1. A right triangle has hypotenuse measuring 40, a leg measuring y, and a leg measuring x opposite a 30 degree angle.
  2. A right triangle has hypotenuse measuring 2 radical 3, a leg measuring x opposite a 30 degree angle, and a leg measuring y opposite a 60 degree angle.
  3. A right triangle has hypotenuse measuring 10, a leg measuring x opposite a 30 degree angle, and a leg measuring y opposite a 60 degree angle.
  4. A right triangle has hypotenuse measuring x, a leg measuring 12, and a leg measuring y opposite a 60 degree angle.
  5. A right triangle has hypotenuse measuring x, a leg measuring y opposite a 30 degree angle, and a leg measuring 2 radical 3 opposite a 60 degree angle.
  6. A right triangle has hypotenuse measuring y, a leg measuring x, and a leg measuring 9 radical 3 opposite a 60 degree angle.
  7. Architecture An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30 degrees angle. To the nearest foot, how far does a person travel from the bottom to the top of the escalator?

    An escalator is 30 degrees from the ground and reaches a height of 25 feet above the ground.
  8. City Planning Jefferson Park sits on one square city block 300 ft on each side. Sidewalks across the park join opposite corners. To the nearest foot, how long is each diagonal sidewalk?

B Apply

Algebra Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

  1. Two right triangles share a leg measuring a. One triangle has other leg c, hypotenuse 7 radical 2, and a 45 degree angle opposite leg a. The other has other leg measuring d, hypotenuse measuring b, and a 30 degree angle opposite leg a.
  2. Two right triangles share a leg measuring a. One triangle has other leg c, hypotenuse 4 radical 3, and a 60 degree angle opposite leg a. The other has other leg measuring d, hypotenuse measuring b, and a 45 degree angle opposite leg a.
  3. Two right triangles share a leg measuring b. One triangle has other leg c, hypotenuse a, and a 30 degree angle opposite leg b. The other has other leg measuring d, hypotenuse measuring 10, and a 60 degree angle opposite leg b.
  4. A trapezoid has side between the right angles measuring 2 radical 3, bottom base measuring b, top base measuring 6, right side measuring a, and angle between top and right sides measuring 60 degrees.
  5. A trapezoid has side between the right angles measuring a, bottom base measuring b, top base measuring 4, left side measuring 3 radical 2, and angle between bottom and left sides measuring 45 degrees.
  6. A trapezoid has side between the right angles measuring 6, bottom base measuring a, top base measuring 8, right side measuring b, and angle between bottom and right sides measuring 45 degrees.
  7. Think About a Plan A farmer's conveyor belt carries bales of hay from the ground to the barn loft. The conveyor belt moves at 100 ft/min. How many seconds does it take for a bale of hay to go from the ground to the barn loft?

    A conveyor belt forms the hypotenuse of a right triangle at a 30 degree angle with the ground extending to 12 feet above the ground.

    • Which part of a right triangle does the conveyor belt represent?
    • You know the speed. What other information do you need to find time?
    • How are minutes and seconds related?

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Table of Contents

Prentice Hall Geometry Chapter 1 Tools of Geometry Chapter 2 Reasoning and Proof Chapter 3 Parallel and Perpendicular Lines Chapter 4 Congruent Triangles Chapter 5 Relationships Within Triangles Chapter 6 Polygons and Quadrilaterals Chapter 7 Similarity Chapter 8 Right Triangles and Trigonometry Chapter 9 Transformations Chapter 10 Area Chapter 11 Surface Area and Volume Chapter 12 Circles Skills Handbook Reference Visual Glossary Selected Answers Index Acknowledgments