Feature Lesson Geometry Lesson Main Lesson 8-3 (For help, go to Lessons 7-1 and 8-2.) ratios , and . Round answers to the nearest hundredth BC AB AC AB BC AC The Tangent Ratio 1. 2. 3. 4. 5. 7. 6. x 3 = 4 7 6 11 x 9 = 8 15 = 4 x 5 x = 7 12 Check Skills You’ll Need Check Skills You’ll Need 8-3
12
Embed
FeatureLesson Geometry Lesson Main Lesson 8-3 (For help, go to Lessons 7-1 and 8-2.) Find the ratios, and. Round answers to the nearest hundredth. BC AB.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
FeatureLesson
GeometryGeometry
LessonMain
Lesson 8-3
(For help, go to Lessons 7-1 and 8-2.)
Find the ratios , and . Round answers to the nearest hundredth.BCAB
ACAB
BCAC
The Tangent RatioThe Tangent Ratio
1. 2. 3.
4. 5. 7.6.x3 =
47
6 11
x9=
8 15 =
4x
5x =
7 12
Check Skills You’ll Need
Check Skills You’ll Need
8-3
FeatureLesson
GeometryGeometry
LessonMain
Lesson 8-3
The Tangent RatioThe Tangent Ratio
Solutions
10 10 2
32
4 38
1. Use the Pythagorean Theorem to find AB: a2 + b2 = c2
4. Find the side length of a 45°-45°-90° triangle with a 4-cm hypotenuse. 5. Two 12-mm sides of a triangle form a 120° angle. Find the length of the third side.
8-3
FeatureLesson
GeometryGeometry
LessonMain
Textbook
FeatureLesson
GeometryGeometry
LessonMain
Lesson 8-3
The Tangent RatioThe Tangent Ratio
Notes
8-3
FeatureLesson
GeometryGeometry
LessonMain
Lesson 8-3
The Tangent RatioThe Tangent Ratio
Notes
8-3
The tangent ratio for an acute angle does not depend on leg lengths of a right triangle. To see why this is so, consider the congruent angles, T and T’, in the two right triangles shown here.
TOW ~ T’O’W’ AA Similarity Postulate
Corresponding sides of ~ triangles are proportional.
tan T = tan T’ Substitute.
' '
' '
OW O W
TO T O
FeatureLesson
GeometryGeometry
LessonMain
Lesson 8-3
The Tangent RatioThe Tangent Ratio
Notes
8-3
If you know leg lengths for a right triangle, you can find the tangent ratio for each acute angle. Conversely, if you know the tangent ratio for an angle, you can use inverse of tangent, tan-1, to find the measure of the angle.
FeatureLesson
GeometryGeometry
LessonMain
tan A2021
= = =oppositeadjacent
BCAC
tan B2120
= = =oppositeadjacent
ACBC
Write the tangent ratios for A and B.
Lesson 8-3
The Tangent RatioThe Tangent Ratio
Quick Check
Additional Examples
8-3
Writing Tangent Ratios
FeatureLesson
GeometryGeometry
LessonMain
To measure the height of a tree, Alma walked 125 ft from the tree and measured a 32° angle from the ground to the top of the tree. Estimate the height of the tree.
The tree forms a right angle with the ground, so you can use the tangent ratio to estimate the height of the tree.