Download Unit 6.1 Tangent Ratio Standard: G.SRT.6 Objective: To use basic

Unit 6.1
Tangent Ratio
Standard:
G.SRT.6
BellWork
∆QRS ~ ∆TUV. Find the value of x.
Objective:
To use basic
trigonometric
functions
defined by
the angles of
a right
triangle.
Right
Triangle
There are three sides in a right triangle that need to be labeled by one of
the acute angle, ____ (________). The side across the right angle is
called the _______________, the side across of θ is called the _________
_____, and the side next to θ is called the __________ _____.
Example 1 Label the right triangle’s sides according to θ.
Checkpoint Label the right triangle’s sides according to θ.
Similar Right
Triangles
Tangent
Ratio
∆ABC ~ ∆GHI ~ ∆RST. Let’s investigate the ratio of the length of the
opposite leg to the length of the adjacent leg.
You may have discovered that in a right triangle, the ________ of
congruent angles are __________. This ratio is called the tangent of the
angle.
Let ∆ABC be a right triangle with A and B.
Example 2 Write the ratios for tan R and tan S.
Checkpoint Write the ratios for tan X and tan Y.
Example 3 Find the tan S and tan R. Write each ratio as a fraction and decimal.
Checkpoint Find the tan D and tan F. Write each ratio as a fraction and decimal.
Example 4
Find the length of AC.
Checkpoint Find the length of RQ.
Example 5 A long ladder is leaning against a building and makes an angle of 56° with
the ground. The base of the ladder is 5 feet from the building. How far up
the side of the building does the ladder reach?
Checkpoint A slide makes a 38° angle with the ground. The base of the slide is 10
feet. How high is the top of the slide above the ground?