Working with Special Right Triangles (Geometry emphasis) Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

Solve the following problems pertaining to special right triangles.

 1. a.  Find x. b.  Find y.   Explanation This is a 30-60-90 triangle. Using the formulas we get: The short leg, x, is 1/2 the hypotenuse. So x = 10. And the long leg, y, is 1/2 the hypotenuse times radical 3. So y = 10 radical 3 which is 17.3 (Trig could also be used in this problem.) a.  Choose: 5 10 14.1 17.3 b.  Choose: 5 10 14.1 17.3

 2. a.  Find x. b.  Find y. a.  Choose: 10 14.1 17.3 b.  Choose: 10 11.5 15.2 17.3 Explanation X is the short leg in a 30-60-90 triangle. The short leg is 1/2 the hypotenuse, so x = 10. The x is also the side of a 45-45-90 triangle. In a 45-45-90 triangle, both legs are equal. So the other leg is 10 units also. This second leg is also the long leg of the 30-60-90 triangle on the bottom. The formula for the long leg is LL=1/2 H times radical 3. Substitute and solve for H. y (or H) equals 11.5

 3 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

 4 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. a.  What is the measure of angle DEC? b.  What is the length of the sides of the rhombus to the nearest integer? c.  What is the length of the longer diagonal to the nearest integer? d. Using your answer from part c and the given diagonal length of 10, find the area of the rhombus. Answer

 5. The lower base angles in this isosceles trapezoid each measure 45º.  The length of the shorter base is 10 inches and the altitude is 8 inches.  Find the length, in inches, of the longer base. Choose: 18 24 26

 6. The shorter base in this trapezoid measures 6 units.   AD = 14 units.  The measure of

 7 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.

 8. Given the picture below, find the lengths of the segments labeled x, y, z and q.

 9. The lengths of the two adjacent sides of parallelogram  ABCD are 8 and 14 units respectively.  If the degree measure of the included angle is 60º, what is the length of the shorter diagonal of the parallelogram. Choose:

 10. A man is walking his dog on level ground in a straight line with the dog's favorite tree.  The angle of elevation from the man's present position to the top of a nearby telephone pole is 30º.  The angle of elevation from the tree to the top of the telephone pole is 45º.  If the telephone pole is 40 feet tall, how far is the man with the dog from the tree?  Express answer to the nearest tenth of a foot. Choose: 1.7 feet 29.3 feet 42.3 feet

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