Understanding the Tangent Ratio: Height Estimation in Right Triangles
In this lesson, we explore the tangent ratio and its application in estimating heights, specifically for measuring objects such as trees. By walking 125 feet away from a tree and measuring a 32° angle from the ground to the top, we can use the tangent ratio to estimate the height of the tree. This lesson includes additional examples and a quick check, covering the tangent ratios for angles A and B. Learn to solve for unknown heights using a calculator and understand the inverse of the tangent function to improve your skills in trigonometry.
Understanding the Tangent Ratio: Height Estimation in Right Triangles
E N D
Presentation Transcript
opposite adjacent BC AC 20 21 tan A = = = opposite adjacent AC BC 21 20 tan B = = = The Tangent Ratio LESSON 8-3 Additional Examples Write the tangent ratios for A and B. Quick Check
Use the tangent ratio. height 125 tan 32° = height = 125 (tan 32°) Solve for height. Use a calculator. 125 32 The Tangent Ratio LESSON 8-3 Additional Examples 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. The tree is about 78 ft tall. Quick Check
47 41 tan R = Find the tangent ratio. 47 41 Use the inverse of the tangent. 47 41 Use a calculator. m R tan–1 So m R 49. The Tangent Ratio LESSON 8-3 Additional Examples Find m R to the nearest degree. Quick Check
