Chapter 5 – Lesson 1 Trigonometry of Right Angles: SOH CAH TOA

Chapter 5 – Lesson 1
Trigonometry of Right Angles: SOH CAH TOA
Minds On
1.
Use the indicated angle to label each side as hypotenuse, opposite and
adjacent.
a) <A
2.
b) <L
The three primary trigonometric ratios are:
Sine (sin) :
Cosine (cos):
Tangent (tan):
_____________
______________
_______________
We can remember these ratios by remembering:
3.
To use the primary trigonometric ratios, what must be true about the
triangle?
Examples:
1.
Determine all unknown side lengths to the nearest unit and all unknown
angles to the nearest degree.
a)
b)
c)
d)
We often use the terms angle of elevation and angle of depression in
trigonometry
Angle of Elevation:
the angle, measured upward, between the horizontal
and the line of sight of the observer
Angle of Depression:
the angle, measured downward, between the
horizontal and the line of sight from an observer to an
object
We need to use these terms and our trigonometric knowledge to solve real-life
problems.
Examples:
1.
From the top of a building 60m high, the angle of depression of a car on
the street is 370. Calculate the distance from the base of the building to
the car.
2.
At a distance of 81m from the base of Big Ben’s clock tower, in London,
England, the angle of elevation to the top of the tower is 500. How tall is
the tower?
3.
For an airplane to land safely, the base of the clouds, or ceiling, above the
airport must be at least 600m. Grimsby Airport has a spotlight that
shines perpendicular to the ground, onto the cloud above. At 1100m
from the spotlight, Cory measures the angle between the spotlight’s
vertical beam of light, to himself, and the illuminated spot on the base of
the cloud to be 550. Cory’s eyes are 1.8m above the ground. With this
cloud ceiling, is it safe for a plane to land at Grimsby Airport?

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