FCP 10
2.1 The Tangent Ratio
When we only have one side of a right triangle we are not able to solve for any other
sides of the triangle. This is where______________________ was introduced. This
is the study of angles and sides of triangles. We will look at the _______________
ratio first.
Chris and Aimee are trying to canoe across Lake Isaac and reach the picnic area.
However, due to the wind, they are getting blown off course. Find the ratio of their
distance off course to the distance of their intended direction and complete the table:
27.1o
Triangle
Picnic
area
Off course
distance
Intended distance
Off Course
Intended
#1
#2
#3
#4
How should the ratio of the off course distance and the intended distance change?
Use your calculator to find the tangent of 27.1o, the angle which they are being blown
off course.
The __________ ratio is found in a right triangle, and shows the ratio of the
_____________ & _____________ sides from the acute angle being considered
Label the following triangles with __________, ___________, _____________
The Tangent Ratio
Tan Θ = ___________________
θ
Find the tangent ratios for each triangle:
12
A
8
Y
13
X
B
5
Given the following Tan ratios, label the following triangles:
Tan Θ =
1
2
Tan Θ =
7
8
Finding Angles with Tangent:
When you wish to find an____________ with tangent we must use our calculator and
press the following button
Try using your calculator to find the following angles.
1. Tan A =
3
4
A = __________
3. Tan A =
5
4
A = __________
2. Tan A =
7
8
A = ____________
4. Tan A = 0.2543
A = __________
We can use this information to find Angles in a right triangle!!!!!
Determine the measures of
G and
J to the nearest tenth of a degree.
Helpful Hint – When completing word problems always draw a picture!!!!!
Example 1:
1. Find the angle at which the solar panel is resting on the roof.
Example 2:
A 10-ft. ladder leans against the side of a building that is 7 ft. tall. What angle, to the
nearest degree, does the ladder make with the ground?
Too much of a TAN!!!!!