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Introduction
Introduction
Trigonometry is based upon ratios of the sides of right triangles.
Trigonometry establishes six ratios called trigonometric functions. In this lesson, we will study the first 3...
sine
cosine, and
tangent
The objective of this lesson is to demonstrate how to use sine, cosine, and tangent are used to calculate the missing sides of right triangles.
Finding Missing Side: Steps
Finding Missing Side: Steps
To find a missing side of a right-angled triangle we need to...
identify/name
(a) the unknown side, and
(b) the given side of the triangle,
in terms of...
opposite, adjacent, or hypotenuse
choose the appropriate ratio,
sin, cos, or tan
use the calculator to identify the angle from the decimal value of the ratio.
Identifying the Missing Angle of a Right Triangle Examples
Identifying the Missing Angle of a Right Triangle Examples
Example 1: Which trig ratio is best to Use?
Example 1: Which trig ratio is best to Use?
Relative to the given angle, we are given...
Hypotenuse (h) = x
Adjacent (A) = 11
Reviewing SOH CAH TOA
Only CAH has adjacent and hypotenuse
So, Cosine is best to use.
Example 2: Which trig ratio is best to Use?
Example 2: Which trig ratio is best to Use?
Relative to the given angle, we are given...
Opposite (o) = x
Adjacent (A) = 13
Reviewing SOH CAH TOA
Only CAH has adjacent and hypotenuse
So, Tangent is best to use.
Example 3: Which trig ratio is best to Use?
Example 3: Which trig ratio is best to Use?
Relative to the given angle, we are given...
Opposite (o) = x
Hypotenuse (H) = 19
Reviewing SOH CAH TOA
Only SOH has adjacent and hypotenuse
So, Sine is best to use.
Summary: Deciding on the trig function to use
Summary: Deciding on the trig function to use
Assign a variable to the unknown side: Using example 3 above, our variable is x.
Deciding on the trig function to use, based on the assumed variable and the information given: Using example 3 above, we will use sine.
Set up the equation:
Sin 40 = x/19
NOTE:
We write SINE(the angle) and NOT sin(a side)
That is, we write sine (40) and NOT sine (19)
Why?: 40 is an angle, and 19 is a side
Isolate the unknown, multiply both sides by 19
19*(Sin 40) = x
19*(0.642 ) = x
12.217 = x
Identifying the Missing Sides of a Right Triangle- Practice
Identifying the Missing Sides of a Right Triangle- Practice
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