Trigonometry

Solutions

Problem Set #3

Complete each triangle :

1. 8/adj = tan(30°) so adj = 8√3 => hypotenuse = 16

2. opposite = 100sin(45) = 100/√2 = adjacent since its isoceles

3. adj = 40

40/hyp = cos(30) => hyp = 40/(√3/2) = 80/ √3 sin(30) = opp/hyp = opp/(80/ √3) => opp =(1/2)(80/ √3)=40/√3

4. A 12” wide board which is 8’ long is lying is attached so that it is at a 30 degree angle to the ground. The sun is directly overhead. What will be the area of the shadow made by the board on the ground?

the length of the shadow is 96cos(30) = 96√3/2 = 48√3 . It’s area is therefore 48√3*12 = 576√3 = 997.66 or about 1000 square inches

5. A truck is driving on a highway in the Rocky Mountains west of Denver. The driver begins to go downhill and sees a sign saying “Caution: 5% slope next 10 miles”. Draw a sketch which accurately reflects this information.

the 5% slope => tan(θ) = .05 where θ is the angle of the highway with the horizontal. The angle is therefore tan^-1(.05) or 2.86° .

Further, in driving down the 10 mile sloped road, the driver will cover 10cos(2.86) horizontal miles or 9.98 miles.

Finally the truck will drop 10sin(2.86) = .499 miles while covering the 10 miles, or just about ½ mile in elevation.