Download Lesson 5.2 Apply the tangent ratio

Lesson 5.2
Apply the tangent ratio
Georgia Performance Standards:
MM2G2a, MM2G2b, MM2G2c
Vocabulary
• Trigonometry is a branch of mathematics that
deals with the relationships between the sides and
angles of triangles and the calculations based on
these relationships.
• A trigonometric ratio is a ratio of the lengths of
two sides in a right triangle.
• In a right triangle, the ratio of the length of the leg
opposite an acute angle to the length of the leg
adjacent to the angle is constant for a given angle
measure.
• This ratio is called the tangent of the angle.
Tangent Ratio:
• Let triangle ABC be a right triangle with acute
angle A. The tangent of angle A (written as tan
A) is defined as follows:
opposite

tan A 
adjacent
A
B
C
BC
AC
Find the tan of
both x and y.
opposite
13
tan x 

 0.1548
adjacent
84
opposite
84
tan y 

 6.4615
adjacent
13
Guided Practice
opposite
tan x 

adjacent
Example 2 Find the value of x
Use the tangent of an acute
angle to find a leg length.
Guided Practice
opposite
tan x 

adjacent
Example 4 Estimate height
using tangent
What if the angle were
72⁰ ?
72⁰
72⁰
Homework
• Using Tangent Ratios
• p.159: 1 – 13