Practice with Trigonometry - Set 2 Topic Index | Algebra Index | Regents Exam Prep Center

Answer the following questions pertaining to right triangles.

 1. A ladder leans against a building.  The foot of the ladder is 6 feet from the building.  The ladder reaches a height of 14 feet on the building. a.  Find the length of the ladder to the nearest foot. Choose: 14       15       15.2       16 b.  Find to the nearest degree, the angle the ladder makes with the ground. Choose: 23        24       66       67 Explanation Part a:  Use Pythagorean Theorem Part b:  one solution is to use tan x = 14/6. and solve for x.

 2 Which statement can NOT  be used to find the length of x? Choose:

 3 From a point on the ground 25 feet from the foot of a tree, the angle of elevation of the top of the tree is 32º.  Find to the nearest foot, the height of the tree.  Answer

 4 The figure shown on the left is a trapezoid.  Using the information given, find the area of this trapezoid to the nearest square unit. Answer

 5 From the top of a barn 25 feet tall, you see a cat on the ground.  The angle of depression of the cat is 40º.  How many feet, to the nearest foot, must the cat walk to reach the barn?  Answer

6.

In the figure on the left, ABCD is a rectangle whose perimeter is 30.   The length of BE is 12.  Find to the nearest degree, the measure of angle E.

 7. a.  Find x. b.  Find y.   Explanation Find x by using sin 30 = x/20. Find y by using cos 30 = y/20 Other solutions are also possible. a.  Choose: 5 10 14.1 17.3 b.  Choose: 5 10 14.1 17.3

 8. This is a hard problem!!! a.  Find x. b.  Find y. a.  Choose: 10 14.1 17.3 b.  Choose: 10 11.5 15.2 17.3 Explanation Using the triangle in the upper right, set up either sin 30 = x/20 or cos 60 = x/20. The triangle upper left is a 45-45-90 triangle where the legs are the same length. Using your answer for x and the lower left triangle, set up sin 60 = x/y. Solve for y.

 9 In the figure on the left, ABCD is a square whose side is 8 units.  Find the length of diagonal AC to the nearest tenth.

 10. In the figure below, ABCD is a rhombus.  The measure of angle A is 150º.  Draw the diagonals so that they intersect at E.  The shorter diagonal measures 10.  Properties of a rhombus:  The diagonals are perpendicular. The diagonals bisect each other. The diagonals bisect the angles. What is the measure of angle DEC? What is the length of the sides of the rhombus to the nearest integer? What is the length of the longer diagonal to the nearest integer? Using your answer from part c and the given diagonal length of 10, find the area of the rhombus.

 11 Choose:

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