1)A billboard d = 61 feet wide is perpendicular to a straight road and is 40 fee

Question

1)A billboard d = 61 feet wide is perpendicular to a straight road and is 40 feet from the road . Find the point on the road at which the angle ? subtended by the billboard is a maximum. (Round your answer to two decimal places.)

        

2)And airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider ? and x as shown in the figure below.

A billboard d = 61 feet wide is perpendicular to a straight road and is 40 feet from the road . Find the point on the road at which the angle ? subtended by the billboard is a maximum. (Round your answer to two decimal places.) And airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider ? and x as shown in the figure below. Write ? as a function of x. The speed of the plane is 389 miles per hour. Find d?/dt when x = 9 and x = 2.

Explanation / Answer

x= 79.50 start with a line for the road and up 'ahead' draw the billboard [89ft] prependicular and 40 ft from the road. now drive down the road till you and the two endpoints of the billboard form an isocelese triangle, that is u r 89 ft from the nearest end of the sign. then use pythagoras to get the distance to level with the sign on the road line
the point at 10 miles above the observer (designate this as O(0,0), the observer, and the plane form a right triangle. plane's coordinate is (-10,0) miles when theta = 45 and observer is (0,-10) constant
plane's coordinate is x = 600 t - 10 (t = 0 when theta = 45)
cot theta = (600 t - 10) / 10 = 60t - 1
take derivate you can get -1/sin^2 ( d theta/dt ) = 60

you can then use dtheta/dt = 60 sin ^2 (theta) to get the rate of change for the angle (radian/hour)
or sin^2(theta) (radian/minute)

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