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Lesson Plans and Worksheets for Geometry

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More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 2, Lesson 32

Student Outcomes

- Students find missing side lengths of an acute triangle given one side length and the measures of two angles.
- Students find the missing side length of an acute triangle given two side lengths and the measure of the included angle.

**Using Trigonometry to Find Side Lengths of an Acute Triangle**

Classwork

**Opening Exercise**

a. Find the lengths of π and π.

b. Find the lengths of π₯ and π¦. How is this different from part (a)?

**Example 1**

A surveyor needs to determine the distance between two points π΄ and π΅ that lie on opposite banks of a river. A point πΆ is chosen 160 meters from point π΄, on the same side of the river as π΄. The measures of β π΅π΄πΆ and β π΄πΆπ΅ are 41Β° and 55Β°, respectively. Approximate the distance from π΄ to π΅ to the nearest meter.

**Exercises 1β2**

- In β³ π΄π΅πΆ, πβ π΄ = 30, π = 12, and π = 10. Find sinβ π΅. Include a diagram in your answer.
- A car is moving toward a tunnel carved out of the base of a hill. As the accompanying diagram shows, the top of the hill, π», is sighted from two locations, π΄ and π΅. The distance between π΄ and π΅ is 250 ft. What is the height, β, of the hill to the nearest foot?

**Example 2**

Our friend the surveyor from Example 1 is doing some further work. He has already found the distance between points π΄ and π΅ (from Example 1). Now he wants to locate a point π· that is equidistant from both π΄ and π΅ and on the same side of the river as π΄. He has his assistant mark the point π· so that β π΄π΅π· and β π΅π΄π· both measure 75Β°. What is the distance between π· and π΄ to the nearest meter?

**Exercise 3**

- Parallelogram π΄π΅πΆπ· has sides of lengths 44 mm and 26 mm, and one of the angles has a measure of 100Β°. Approximate the length of diagonal π΄πΆΜ Μ Μ Μ to the nearest millimeter.

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