Chapter 8: Q. 59 (page 536)
What do you do first if you are asked to solve a triangle and are given two sides and the included angle?
To solve a triangle with two sides and the included angle, first we will find the third side of the triangle using the Law of Cosines.
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If three sides of a triangle are given, the Law of _________ is used to solve the triangle.
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 15ยฐ, how fast is the truck traveling? Express the answer in feet per second and in miles per hour.
(b) If the angle measures 20ยฐ, 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?
Cost of a Triangular Lot The dimensions of a triangular lot are 100 feet by 50 feet by 75 feet. If the price of such land is $3 per square foot, how much does the lot cost?
Mollweideโs Formula For any triangle, Mollweideโs Formula (named after Karl Mollweide, 1774โ1825) states that
Derive it.
[Hint: Use the Law of Sines and then a Sum-to-Product Formula. Notice that this formula involves all six parts of a triangle. As a result, it is sometimes used to check the solution of a triangle.]
Rework Problem 7 under the same conditions except that, at time t = 0, the object is at its resting position and moving down.
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