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Geometry - Chapter 8 Practice Test
For the triangles ABC, MKR and EJH shown above, determine the stated value and give your answers as a fraction or an angle.
**1. cos(Z) =
- tan(Q) =
- sin(P) =
- tan** - 1
**2. sin(Y) =
- cos(Y) =
- tan(W) =
- cos** - 1
9. A cable is attached from the ground to the top of a telephone pole. The length of the cable is 46 ft. The connection at the ground level forms an angle of elevation of 74°. How tall is the telephone pole? Draw a picture to show your logic. 10. An airplane begins to descend at an angle of depression of 9 ° so that it can land at an airport that is 42 miles away (the horizontal distance as measured on the ground). How far is the plane from the airport? Draw a picture to show your logic. Note : The distance being asked for is the direct distance measured in a straight line from the plane down to the airport.
12. Fill in the blanks. For each answer, draw a picture to the side to show why your answer is correct. cos( 61 ° ) = sin( 29 ° ) sin( 37° ) = cos( 53 ° ) 13. For the triangle shown below, determine the measure (size) of the unknown angles. For each angle, give your answer out to three decimal places. Now, obviously you could use trig to solve for one angle and then determine the other angle by using simple knowledge about the angles in a triangle. However, what we want you to do is the following: Solve for m
∠X using either the sine or cosine function.
Then solve for m
∠Y using the tangent function.
After solving for both angles, you must check your answers by adding your two answers together.
14. Plot the following points and use the slope formula to determine whether SGT is a right triangle for the given vertices. S = (– 4 , 2 ) G = ( 2 , 6 ) T = ( 2 , – 7 ) 15. The sides of triangle ABC have lengths as follows: AB = 27 BC = 45 AC = 36 Is the triangle a right triangle? If so, which vertex is the right angle? 16. The square below has sides X = 10 2. Determine the length of the diagonal Y.
