Observe the triangle below. Solve for the missing side. 12 5 X=?

SWBAT… :

SWBAT… Solve for the missing sides of triangles using trigonometry and the Pythagorean theorem.
Use the vector cheat sheet to find the components of a velocity vector or to find its magnitude.
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Docket :

Docket HW
Do Now
Trig Review
Pythag Review
Vector Cheat Sheet
HW

Docket :

Docket HW
Do Now
Trig Review
Pythag Review
Vector Cheat Sheet
HW

Slide 6:

Lucy and her friend are working at an assembly plant making wooden toy giraffes. At the end of the line, the giraffes go horizontally off the edge of the conveyor belt and fall into a box below. If the box is 0.6m below the level of the conveyor belt and 0.4 meters away from it, what must the horizontal velocity of the giraffes be as they leave the belt if they are to land in the box? Picture X Problem Y Problem Trig .6m .4m Vi=?

Slide 7:

You are visiting a friend from elementary school who now lives in a small town. One local amusement is the ice-cream parlor where Stan slides his completed ice-cream sundaes down the counter at a constant speed of 2.0 m/s to the servers. If the servers catch the sundaes .07 horizontal meters away from the counter, how far have the sundaes fallen before they are caught? Picture X Problem Y Problem Trig ?m .07 m Vi=2.0m/s

Docket :

Docket HW
Do Now
Trig Review
Pythag Review
Vector Cheat Sheet
HW

Do Now :

Do Now Observe the triangle below. Solve for the missing side. 12 5 X=? legs Hypotenuse

Docket :

Docket HW
Do Now
Trig Review
Pythag Review
Vector Cheat Sheet
HW

Motivation :

Motivation The cliff problems we’ve been doing are fine, but you seem to have the hang of them already.
What if instead of an old lady running off the roof horizontally, she JUMPS off of the roof? 4 m/s ? m 22 m

What if we have a velocity that is not perfectly horizontal? :

What if we have a velocity that is not perfectly horizontal? The velocity belongs in BOTH the x and y problem.
But not all of the velocity is in x, and not all of it is in y.
We have to figure out how to split up the velocity vector, so that it has pieces in both x and y

Pythagorean Theorem :

Pythagorean Theorem The Pythag Theorem helps to calculate a side of a triangle when you have two others.
For our purposes, you will only be using the this theorem to find the hypotenuse of a triangle.

Example :

Example Solve for the hypotenuse of the triangle below.

You Try! :

You Try! Solve for the hypotenuse of the triangle below.

Docket :

Docket HW
Do Now
Trig Review
Pythag Review
Vector Cheat Sheet
HW

Triangles! :

Triangles! SOHCAHTOA sin cos tan opposite opposite Hypotenuse adjacent adjacent Hypotenuse

Solving for sides/angles of triangles :

Solving for sides/angles of triangles 10 60º x It looks like if we are looking for the opposite side, it’s the hypotenuse times the sin of the angle.

Solving for sides/angles of triangles :

Solving for sides/angles of triangles 12 40º x It looks like if we are looking for the adjacent side, it’s the hypotenuse times the cos of the angle.

You Try! :

You Try! 21 19º x

What if you are looking for an angle? :

What if you are looking for an angle? Inverse functions!
For our purposes, we will only use inverse tan.

You Try :

You Try

A Vector Cheat Sheet! :

A Vector Cheat Sheet! Let’s make it general, given a vector V (it will be a velocity vector), let’s relate its x-piece, its y-piece, and its angle all together.

A Vector Cheat Sheet! :

A Vector Cheat Sheet!

Practice :

Practice Find V and ᶱ

What if my vector doesn’t look like that? :

What if my vector doesn’t look like that? No matter which way the vector points, you can still do the same thing, just be careful about what is opposite and what is adjacent!

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