Section. 6.2 Exercises Find the exact value of the six trigonometric ratios of the shaded angle ! in the triangle.
Sketch two possible triangles (with different side lengths) with acute angle ! and whose sin (! ) = 513 .
Evaluate without using a calculator. 2
! !!$ !!$ !!$ ! ! $$ #" sin #" 3 &% cos #" 4 &% ' sin #" 4 &% cos #" 3 &% &%
Solve the following right triangle twice, first assuming the angle is measured in degrees, then assuming the angle is measured in radians.
1
Section. 6.2 Exercises Express the length x in terms of trigonometric ratios of the shaded angle ! . Angles CDA, ABD, and CAB are all right angles.
Find the length of the side labeled x. Round to three decimal places.
The angle of elevation (from the ground to the top of the building) to the top of the Empire State Building in New York is found to be 11 degrees at a distance of 1 mile form the base of the building. Use this information to find the height of the Empire State Building. (1 mile = 5,280 feet)
A woman standing on a hill sees a flagpole that she knows is 60 feet tall. The angle of depression to the bottom of the pole is 14 degrees and the angle of elevation to the top of the pole is 18 degrees. Find her distance from the flag pole.
2
Section. 6.2 Exercises To estimate the height of a mountain, the angle of elevation is measured to be 32 degrees. One thousand feet closer to the mountain (at the same elevation), it is found that the angle of elevation is 35 degrees. Estimate the height of the mountain.
Here is a modern method of finding the radius of the earth. A satellite that is 600 miles above the earth forms an angle with the horizon of 60.276 degrees. Use this information to find the radius of the earth.
Use your calculator to determine if the Use your calculator to determine if the following is true or false. (Note: What is the following is true or false. measurement of the angle in this problem?) sin 70 ! sin 50 = sin 20 1 sin ( 50 ) = sin ( 25) 2
( )
3
( )
( )
Section. 6.2 Exercises
4