Daily Check

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Daily Check
For the triangle at the right, find the sine,
cosine, and tangent of angle z.
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Math II
UNIT QUESTION What patterns can I find in right
triangles? Standard MM2G1, MM2G2 Todays
Question How do you use trig ratios to find the
all the missing parts of a triangle? Standard
MM2G2.a,b
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hypotenuse
hypotenuse
opposite
opposite
adjacent
adjacent
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Using a Calculator
If you know the value of a specific trig ratio
for an unknown angle, you can calculate the
measure of the angle.
For example, if for the triangle below
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On most calculators written above the Sin, Cos
and Tan buttons are
These are used to find the angle when you already
know the value for the ratio. On the calculator
there will be a button, sometimes it reads 2nd,
that will need to be pushed before you push the
Sin, Cos or Tan button. This button will allow
you to do the function above the button.
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Using a Calculator
On the calculator enter 0.375 the hit the 2nd
button and then the Sin button.
The number 22.02 should be displayed. This is
the angle that has a Sin value of 0.375
Then, that means
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On a graphics calculators you will enter it just
like it reads in the equation.
Then you can calculate the angle value.
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Problem-Solving Strategies
Scenario 1) You are given 2 sides of the
triangle. Find the other side and the two acute
angles.
1A. Use the Pythagorean theorem to find the 3rd
side.
1B. Use an inverse trig function to get an angle.
Then use that angle to calculate the 3rd angle.
Sum of the angles 180º
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Problem-Solving Strategies
Scenario 1) You are given 2 sides of the
triangle. Find the other side and the two acute
angles.
2A. Use an inverse trig function to get an angle.
Then use the sum of the angles 180º to find the
3rd angle.
2B. Use a trig ratio using one of the two angles
to get the 3rd side.
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Problem-Solving Strategies
Scenario 2) You are given an angle and a side.
Find the other angle and the two other sides.
1A. Use 2 different trig ratios from the given
angle to get each of the other two sides.
1B. Use the sum of the angles to get the 3rd
angle.
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Problem-Solving Strategies
Scenario 2) You are given an angle and a side.
Find the other angle and the two other sides.
2A. Use the sum of the angles to get the 3rd
angle.
2B. Use 2 different trig ratios from the 3rd
angle to get each of the other two sides.
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Problem-Solving Strategies
Scenario 3) You are given all 3 sides of the
triangle. Find the two non-right angles.
1. Use 2 different trig ratios to get each of the
angles.
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Problem-Solving Strategies
Scenario 3) You are given all 3 sides of the
triangle. Find the two non-right angles.
2A. Use a trig ratio to get one angle.
2B. Use the sum of angles to get the 3rd angle
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Angle of Elevation/Depression
Sometimes when we use right triangles to model
real-life situations, we use the terms angle of
elevation and angle of depression.
If you are standing on the ground and looking up
at a hot air balloon, the angle that you look up
from ground level is called the angle of
elevation.
If someone is in the hot air balloon and looks
down to the ground to see you, the angle that
they have to lower their eyes, from looking
straight ahead, is called the angle of depression.
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Angle of Elevation/Depression
If you look up 15º to see the balloon, then the
person in the balloon has to look down 15º to see
you on the ground.
Angle of elevation Angle of depression.
Balloon
Angle of depression 15º
You
Angle of elevation 15º
Notice that in this situation, the one of the
legs that forms the right angle is also the
height of the balloon.
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Draw a Picture
When solving math problems, it can be very
helpful to draw a picture of the situation if
none is given.
Here is an example.
Find the missing sides and angles for Triangle
FRY. Given that angle Y is the right angle, f
68, and y 88.
The picture helps to visualize what we know and
what we want to find!
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Homework Page 174 5-21 (odd)