Trigonometry Problem

Question

A typical drag road is 402 metres long. Suppose a set of bleachers 3m deep is set up 20 m away from the track.

a) Suppose you are sitting in the front middle seat. Write an equation that represents distance, d, of the track visible by turning your head an angle of θ in one direction. Include the domain for this scenario.

b) Sketch the graph of the equation you determined in a) over the domain you gave. Accurately label both axes with appropriate scales.

c) Determine the maximum and minimum values of d and θ.

Answer 1

let angle Theta = x

construct a right triangle, d/2 = opposite side, 20 meters = adjacent side

tangent of x = tanx = d/2/20=d/40

d= 40tanx= total distance you can see turning you head an angle of x in either direction

tanx= d/40

x = tan^-1( ) = tan^-1( ) = about degrees

range of d is 0 to 402 meters

domain of x is 0 degrees to degrees

turn your head more than degrees and you're looking beyond the end of the 402 meter track