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Chapter 8: Q. 30 (page 535)
Solve each triangle.
The required triangle is
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Calculating Distances at Sea The navigator of a ship at sea spots two lighthouses that she knows to be 3 miles apart along a straight seashore. She determines that the angles formed between two line-of-sight observations of the lighthouses and the line from the ship directly to shore are 15掳 and 35掳. See the illustration.
(a) How far is the ship from lighthouse P?
(b) How far is the ship from lighthouse Q?
(c) How far is the ship from shore?
Find an equation for the circle with center at the point and radius 3. Graph this circle.
Finding the Length of a Ski Lift Consult the figure. To find the length of the span of a proposed ski lift from P to Q, a surveyor measures DPQ to be 25掳 and then walks off a
distance of 1000 feet to R and measures PRQ to be 15掳. What is the distance from P to Q?
Find an exact value of each expression, without using a calculator
A state trooper is hidden 30 feet from a highway. One second after a truck passes, the angle between the highway and the line of observation from the patrol car to the truck is measured. See the illustration.
(a) If the angle measures 15掳, how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
(b) If the angle measures 20掳, how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
(c) If the speed limit is 55 miles per hour and a speeding ticket is issued for speeds of 5 miles per hour or more over the limit, for what angles should the trooper issue a ticket?
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