A bridge is to be built across a small lake from a gazebo to a dock see figure The bearing from the gazebo to the dock is S 41 W From a tree 100 meters from the gazebo the bearings to the gazebo and the dock are S 74 E and S 28 E respectively Find the distance from the gaze ID: 576628
Download Presentation The PPT/PDF document "Bridge Design" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Bridge Design
A bridge is to be built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S 41 W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74 E and S 28 E, respectively. Find the distance from the gazebo to the dock.Slide2Slide3
Finding the Area – Using the Law of Sines
A
B
C
c
ba
* Draw an altitude from vertex B.Slide4
Are there unique triangles with the side and angle measures given above? Why?
Why can’t the Law of
Sines be used to determine the measures of the missing angles and/or sides?Slide5
Complete the Law of Cosines
Activity …Slide6
NOTES (Law of Cosines 16.2)
LAW OF COSINES: a2 = b2 = c2 = Slide7
Use Law of Cosines to solve for Cos A.Slide8
Law
of Cosines (solving for angles) Cos A = Cos B =
Cos C =Slide9
Solve for all missing information …Slide10
EXAMPLE 1:
Two ships leave at 4pm. One is headed at a bearing of N 38 E and is traveling at 11.5 miles per hour. The other is traveling at 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6pm?Slide11
EXAMPLE 2:
The distance on a map from the airport in Miami, FL, to the one in Nassau, Bahamas is 295 kilometers due East. Bangor, Maine is northeast of both cities; its airport is 2350 kilometers from Miami and 2323 kilometers from Nassau. What bearing would a plane need to take to fly from Nassau to Bangor?