Download Day 2- Trig solving for sides

Graph of the Day
Red
Slope
Y intercept
Point of intersection
Blue
Graph these 2 lines and find the
point of intersection
y=
3
𝑥
2
y=-
–3
1
𝑥
4
+4
Trigonometry
Learning Goals
• I can calculate the trigonometry ratios given an angle
• I can calculate the side length given the trigonometry
ratios using SOCAHTOA or Pythagorean
Remember
• How to identify the sides
of a triangle:
• Hypotenuse is always the
longest side and
opposite the 90° angle.
θ
hypotenuse
Remember
• How to identify the sides
of a triangle:
• The adjacent side is the
one right beside the
angle θ (that is not the
hypotenuse)
θ
hypotenuse
adjacent
Remember
• How to identify the sides
of a triangle:
• The opposite side is
opposite the angle θ.
• It is the one side that does
not touch the angle θ
θ
hypotenuse
opposite
adjacent
Remember
Soh Cah Toa
Sin θ =
𝑂
𝐻
=
4
𝐻
Tan θ = =
3
4
Cos θ =
𝐴
𝐻
=
3
5
𝑂
𝐴
θ
5
4
3
Soak a toe
Find a side length
• If we know an angle and a side, we can
calculate a side length.
• Which side is x? opposite, adjacent or
hypotenuse?
36.87°
5
3
x
Find a side length
• So to find x (adjacent) we can use
• Cos 36.87° =
𝑥
5
36.87°
5
• Cos 36.87°(5) = x
• x = 3.99999 (round up to 4)
3
x
Find a side length
• Or to find x (adjacent) we can also use
• Tan 36.87° =
3
𝑥
36.87°
5
• Tan 36.87°(x) = 3
3
• x = 𝑇𝑎𝑛 36.87°
• x = 3.99999 (round up to 4)
3
x
One more triangle
• What is x?
• x is hypotenuse
• 2 is opposite
2
Type equation
here.
• So we must use Sin θ =
• Sin 53.13° =
•x =
2
sin 53.13°
2
𝑥
𝑂
𝐻
x = 2.5
y
x
53.13°
One more triangle
• What is y?
2
• y is adjacent
• So we can use Cos θ =
• Cos 53.13° =
𝐴
𝐻
or Tan θ =
𝑦
2.5
• y = Cos 53.13°(2.5) y = 1.5
𝑂
𝐴
Type equation
here.
• 2 is opposite and 2.5 is hypotenuse
2.5
y
53.13°
Textbook Questions
• Pg 71 # 3,4,5