Download sohcahtoa

SOHCAHTOA
Take a moment to look at the following picture and then think about
the questions below:




What type of triangle is this? How do you know?
What do you think the “θ” means?
Which side is the hypotenuse?
If I told you one of the legs would be labeled as opposite and the
other as adjacent, which would be which in this picture?
Write your thoughts in your notebook or discuss them with a neighbor.
Let’s watch the first 1:50 of this video and then think back to your
answers to the questions above.
http://www.youtube.com/watch?v=VRz2d5yedsg
Definitions:
 θ
o The Greek letter Theta which is used to represent an
unknown angle in triangles
 Opposite Leg
o The leg across from θ in a right triangle
 Adjacent Leg
o The leg beside θ in a right triangle
 Sine Ratio
o The ratio of the lengths of the opposite side to the
hypotenuse
o Often called sin
 Cosine Ratio
o The ratio of the lengths of the adjacent side to the
hypotenuse
o Often called cos
 Tangent Ratio
o The ratio of the lengths of the opposite side to the adjacent
side
o Often called tan
Equations:
 Sine Ratio
sin 𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
 Cosine Ratio
cos 𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
 Tangent Ratio
tan 𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Example:
 For the triangle below, determine the sine, cosine and tangent
ratios.
θ
o Before we start, let’s sort out the hypotenuse, opposite and
adjacent legs for the angle θ.
The 4.9 side is across from the box indicating a right angle so
that must be the hypotenuse.
The 2.8 side is across from θ so it must be the opposite leg.
The 4.0 side is beside θ so it must be the adjacent leg.
Hypotenuse
Opposite Leg
θ
Adjacent Leg
o To find the sine ratio we need the opposite leg and
hypotenuse to put into its equation.
opposite = 2.8
hypotenuse = 4.9
sin 𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=
2.8
4.9
= 0.57
o To find the cosine ratio we need the adjacent leg and
hypotenuse to put into its equation.
adjacent = 4.0
hypotenuse = 4.9
cos 𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=
4.0
4.9
= 0.82
o To find the tangent ratio we need the opposite and adjacent
legs to put into its equation.
opposite = 2.8
adjacent = 4.0
tan 𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
=
2.8
4.0
= 0.70
Let’s try a few together:
 A right triangle has a hypotenuse of 5, an opposite side of 3 and
an adjacent side of 4.
o Draw a diagram of this triangle.
o Determine the sine ratio.
o Determine the cosine ratio.
o Determine the tangent ratio.
Consider the following:
 What is the sine ratio for a right triangle that has a hypotenuse of
15, an opposite side of 9 and an adjacent side of 12?
 How does this triangle compare to the previous example?
 How does the ratio compare?
 What could you say about triangles like these two?
Write your thoughts in your notebook or discuss them with a neighbor.
Let’s see what our thoughts are for these questions.
Key Point:
 In similar right triangles, the sine, cosine and tangent ratios will be
equal despite the size difference of the sides.
Try the question below on your own. If you can complete it correctly,
you should be ready for the practice work.
 Determine the tangent ratio of
this triangle.
(2.4)
Practice
Complete the Trigonometric Ratios Practice handout.