Multiple Choice Practice - Pythagorean Theorem & Trigonometric Functions Integrated Algebra Level Algebra Index | Regents Exam Prep Center

 Also available in Hardcopy (.pdf): Pythagorean Thm and Trigonometry

Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use your graphing calculator when working on these problems.

1.   Two sides of a triangle measure 10 inches and 6 inches. Which of the following choices for the length of the third side will make the triangle a right triangle?
[1]  4 inches             [2]  7 inches             [3]  8 inches         [4]  9 inches

2.  The side of a square measures 6 cm. What is the exact length of the diagonal of the square?

[1]  cm.             [2]  cm.           [3]  cm.         [4]  cm.

3.  The length of the hypotenuse of a right triangle is 32 inches and the length of one of the legs is 18 inches. What is the length, to the nearest tenth of an inch, of the other leg of the triangle?

[1]  36.7 inches         [2]  28.4 inches         [3]  26.5 inches    [4]  25.4 inches

 4.  A light post, shown at the right, is set in concrete and supported with a guy wire while the concrete dries. The length of the guy wire is 10 feet and the ground stake is 4 feet from the bottom of the light post. Which equation could be used to find the height of the light post, x, from the ground to the top of the light post?   [1]  [2]  [3]  [4]

 5.  In the diagram at the right, MH = 15, HT = 13, and AT = 5. Find MA.  [1]  8 [2]  9 [3]  12   [4]  14

6.  In triangle MAP, the measure of angle P is 90º, MA = 68, MP = 32 and PA = 60. Which ratio represents the cosine of <A?

[1]  60/68                  [2]  32/68                 [3]  32/60             [4]  60/32

 7.  In the diagram shown at the right, what is the value of x to the nearest whole number? [1]  8 [2]  9 [3]  10 [4]  13

8.  In right triangle PQR, PR = 26, PQ = 10, QR = 24, and m<Q = 90. Find, to the nearest degree, the measure of angle P.

[1]  22                    [2] 68                      [3] 23                       [4] 67

 9.  Which of the following equations can be used to find the value of x in the diagram at the right? [1]                  [2]  [3]                 [4]  All choices can be used.

10.  The choices below contain the lengths of the sides of four separate triangles. Which of the choices is NOT a right triangle?

[1]  12, 16, 20                       [2]  15, 36, 39

[3]  20, 24, 26                       [4]  30, 40, 50

 11.  A light post, shown at the right, is set in concrete and supported with a guy wire while the concrete dries. Find, to the nearest degree, the angle of elevation of the top of the post made by the guy wire from the stake in the ground. [1] 66º [2] 24º [3] 22º [4] 64º

 12.  From a point, G, on the ground, the angle of elevation of an airplane is 21º. The altitude of the plane is 2200 meters. What is the distance from point G to the airplane, to the nearest tenth of a meter? [1] 2356.5 meters [2] 3241.4 meters [3] 5731.2 meters [4] 6138.9 meters

 13. Find to the nearest degree, the number of degrees in the angle labeled , in the diagram at the right. (Hint: this is a two step problem. Use the small triangle on the left to help find needed information.) [1]  32º [2]  44º [3]  48º [4]  52º

14.
If the legs of a right triangle are 28 units and 45 units, find the exact number of units in the  hypotenuse.

[1]  48                    [2]  51                  [3]  53                  [4]  67

15.  The hypotenuse of a right triangle has a length . If one of the legs is , find the exact value of the other leg.

[1]                     [2]                  [3]               [4]

 16.  Find the area of the right triangle shown at the right. [1]  56 square units [2]  84 square units  [3]  168 square units [4]  175 square units

 17.  Right triangle ABC is shown at the right. Find the value of cos(B) to the nearest tenth. (Hint: find the hypotenuse first.) [1]  0.6                      [2]  1.3   [3]  0.8                      [4]  1.7

18.  The legs of an isosceles right triangle each measure 4 units. Find the exact length of the hypotenuse.

[1]                      [2]                [3]                 [4]

 19.  A right triangle is shown at the right. Find the value of x.   [1]  4 [2]  6 [3]  8 [4]  9

 20.  A plane has traveled 24 miles on a course heading 52º east of north. How far north (x) has the plane traveled at this point? Express answer to the nearest hundredth of a mile. [1]  12.94 miles [2]  14.78 miles [3]  18.91 miles [4]  21.72 miles

Contact Info: D. Roberts at donrob@twcny.rr.com