Applying Tangents

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New York State Common Core Math Geometry, Module 2, Lesson 29

Worksheets for Geometry

Student Outcomes

  • Students understand that the value of the tangent ratio of the angle of elevation or depression of a line is equal to the slope of the line.
  • Students use the value of the tangent ratio of the angle of elevation or depression to solve real-world problems.

Applying Tangents


Opening Exercise

a. Use a calculator to find the tangent of 𝜃. Enter the values, correct to four decimal places, in the last row of the table. b. The table from Lesson 29 is provided here for you. In the row labeled sin θ/cos θ, divide the sine values by the cosine values. What do you notice?

Example 1

Scott, whose eye level is 1.5 m above the ground, stands 30 m from a tree. The angle of elevation of a bird at the top of the tree is 36°. How far above ground is the bird?

Example 2

From an angle of depression of 40°, John watches his friend approach his building while standing on the rooftop. The rooftop is 16 m from the ground, and John’s eye level is at about 1.8 m from the rooftop. What is the distance between John’s friend and the building?

Exercise 1

Standing on the gallery of a lighthouse (the deck at the top of a lighthouse), a person spots a ship at an angle of depression of 20°. The lighthouse is 28 m tall and sits on a cliff 45 m tall as measured from sea level. What is the horizontal distance between the lighthouse and the ship? Sketch a diagram to support your answer.

Exercise 2

A line on the coordinate plane makes an angle of depression of 36°. Find the slope of the line correct to four decimal places.

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