Mili: Trying out for My License

Learning how to use Cosine by Kathena Sanders

What is cosine? How is it used?

Cosine is a trigonometric function that is equal to the ratio of the side adjacent to an acute angle to the hypotenuse.

This function is used when you are trying to find the length of a segment.

Here are some of the formulas:


a2 = b2 + c2−2bcCosA

b2 = a2 + c2−2acCosB

c2 = a2 + b2−2abCosC


Here is an example problem:

A triangle has the segments of A, B, and C and it also has the sides of A, B, and C. Segment B has the degree of 76 degrees, a has a measurement of 8 and c has a measurement of 5. Now you must plug in the numbers given using the formula give above. The last number you plug in must be equivalent to the one you began with. You need to find the measurement of side b.


Hint: 76 degrees

This is the answer you should have received: approx. 8 (8.36)

You would have received this answer by following these steps:

1.) a=5, c=8, and B=76 degrees

2.) You plug the given numbers above into the formula

b^2=c^2+a^2-2(c)(a)CosB

76 degrees^2= 8^2+5^2-2(8)(5)Cos76

-note that you have plugged in all numbers and as a result the beginning number is the same as the ending number (76) thus meaning you plugged in all numbers correctly.

3.) Afterwards you sole the equation in your calculator

4.) Finally, you square root and you will receive your answer

-note you may have to have an approx. sign if it is close but not equal to that answer given.

Everyday At HCS Early College High School in Mrs. Wilson's Room

Main Problem (Project Problem)

Following the information above and using the example I showed you earlier as a guideline solve this equation about Mili in her quest of receiving her drivers license.


Story Plot:

Mili is trying out for her license today. She really wants to make the best impression on her instructor as possible in order to improve her chances of receiving her license. Mili's instructor has given her directions to drive from Conway DMV to downtown Conway bridge. She was told to take two streets named Casey Street and Peach Street; one for the way to the destination and one for the way back. She sees that Street A (Casey Street f 110 ft and that Street B (Peach Street) has a distance of 115 ft. She decides it would be better to to take a short cut in order to show her instructor her driving skills. To make sure the shortcut she wants to take is in fact shorter then streets A and B she wants to calculate the distance of the shortcut (Street C) and determine whether its distance compared to Streets A and B is shorter. Show your work, label, and afterwards explain your steps.


Hint:

Angle measurement of street c is 53 (use Cosine)


Steps:

1.) Find the given measurements

2.)Plug in measurements into the formula

3.) Square root your answer


Results:

You should have gotten the answer of 100.

The measurements given were a=110 ft, b= 115 ft, and 53 degrees.

You were to plug those measurements into the formula of c^2=a^2+b^2-2abCosC and you would have received this equation "53 degrees^2=110^2+115^2-2(110)(115)Cos53degrees. This equation after calculating it you would have gotten the answer of 10099.0799. You would have then square rooted this answer and got 100. This answer (100 ft) is the distance of street C. Comparing this answer to or Street C to the other two distances of Streets A and B would have confirmed the fact that Street C is shorter and is a short cut.

Mili: Street Distances

(Triangle with Measurements & Angles)

Law of Cosines, Example 1