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 Amsco Integrated Algebra I: Applications of the Tangent Ratio
This is a free lesson from our course in Amsco's Integrated Algebra
In this lesson you’ll learn to find the tangent of an angle and how tangent ratio is often used to make indirect measurements when the measures of a leg and an acute angle of a right triangle are known. Here earlier learning about how to find the measure of an angle in a right triangle when you know the measures of the two legs will also help. It explains about angle of elevation, angle of depression and how to solve problems using them. The angle of elevation is the angle determined by the rays that are parts of the horizontal line and the line of sight when looking upward, and angle of depression is the angle determined by the rays that are parts of the horizontal line and of the line of sight when looking downward. E.g. when a telescope is used to sight the top of a telephone pole, the instrument is elevated i.e. tilted upward from a horizontal position is the case of angle of elevation. (More text below video...)
People who saw this lesson also found the following lessons useful:
The Pythagorean Theorem
Applications of the Sine and Cosine Ratios
(Continued from above) Similarly when you sight a boat from a cliff, it is depressed i.e. tilted downward from a horizontal position is the case of angle of depression. For example: Given- In a case of a wheelchair ramp to the emergency exit of the Health Care Center is with 5 feet high landing and that angle of elevation the ramp makes with the ground cannot be greater than 7°. You need to work out what is the minimum distance from the landing that the ramp should start? To solve the above problem, first draw a diagram.  mA = 7°
adjacent leg = x feet
opposite leg = 5 feet
Now substitute these values into the definition of tangent.

tan 7° = 5/x
(tan 7°)(x) = 5 multiply each side by x.
x = Divide each side by tan 7°.
x = 40.72191
The ramp should begin about 40.7 feet from the landing.
The video above will help understand using several examples, application of the tangent ratio to solve the problems.


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