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Transcript of Trigonometry
prezi by Mary & Ty
class period 3
What is Trigonometry?
-the study of triangles by using functions to study properties of triangles
the main formula
How did we use this formula as a carpenter?
To fix a wobbling door we had to insert a wire support. We know that the width of the door was 3 feet and 8 feet high. The wire was going to be placed diagonally, so we used the Pythagorean theorem. You need to add 3 squared + 8 squared = c squared. So, 9+64 =c squared. 73 = c squared then the square root of 73 is 8.5 feet. What did you get?
In problem two, there was a house that a carpenter was cutting boards for. At the top of the house where the sides meet it forms a 90 degrees angle. The width of the house is 8 yards. It is common sense that the corners where the roof meets the house was 45 degrees each. Which means that a=b. We did the inverse of the Pythagorean theorem by putting 8 squared in the c squared spot. The carpenter needs to cut his boards to = 5.6 yards. What did you get?
there are three ratios
Lets get our tan on!
tanA opposite leg over the adjacent leg
How did we use the ratio?
In problem three there was a handicap ramp you had to build. 3 feet high and when the ramp touches the ground it needs to be at a 7 degree angle. First set up the ratio which is tan7 degrees = 3/x. Tan 7 degree times x =3. x=3/tan 7 degree. x=24.4 So, the length of the ramp will need to be 24.4 feet. What do you think?
sine or cosine
Cos A~the adjacent leg over the hypotenuse
How did we use the formula?
To find the other length of the wall in problem four we used the cosine ratio. To find the length of the vertical line you need to set your problem up cos63 degrees = y/10. 10x cos63 = y. Y=4.5ft. So, the length of the adjacent side is 4.5 feet
Thanks for your attention!! Your tan looks fantastic!
It's not a sin
sin A=opposite leg over the hypotenuse
How did we use the formula?
In problem four you have to put molding in a triangular room without using a tape measure. One corner was 90 degrees and the hypotenuse was 10 feet tall and one corner was 63 degrees. We used the sine ratio to determine that the length opposite the hypotenuse is 8.9 feet. What do you think?
Pythagorean theorem ~The square root of a or b is equal to the square root of c.
When would you use the pythagorean theorem?
If you have a square or triangle you would like to find the lengths of the sides or the hypotenuse.
When would you use the sine function?
If there is a triangle or square that gives you the hypotenuse length or the length of the opposite side.
When would you use this function?
You use this function to find a missing degree or length of a right triangle. You have to use the hypotenuse and the adjacent side.
You use the function when you are trying to get the angle or the lengths of a side. You do not use the length of the hypotenuse.