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# Honors Activity

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## Natalie Bailey

on 21 May 2014

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#### Transcript of Honors Activity

Honors Extension Activity
Problem 1
Question:

A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims, that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.

Problem 2
Question:
An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.

Problem 3
Question:
There are two fruit trees located at (3,0) and (–3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.
Problem 4
Let’s say that triangle ABC represents the triangular section of lawn that will be converted to river rock. The opposite of angle A is a, the opposite of angle B is b, and the opposite of angle C is c. We are solving for line c. Maurice wants to use the law of Cosines to solve for the missing angle of triangle ABC. If they had the measurements for lines a and b only, then you would only be able to solve for line c with the law of cosines. Johanna wants to use the law of Sines to solve for line c. If only the measurements for lines a, b, and angle A were known, then you could use law of sines to solve for line c. As long as 2 sides and an opposite angle measure are know, both the law of Sines and the law of Cosines can be used to determine the missing side length c.