Solving  Right Triangles 

Designed by: Melanie B. Moorer     School: Dreher High School 

Grade Level: 10-12    Subject: Mathematics (Geometry or Trigonometry) 

Core Curriculum Objective: Solve right triangles using basic trigonometric functions. 

Overview:  Students will work independently and in small groups to develop strategies to solve right triangle using basic trigonometric functions. Students will use various instructional strategies such as: demonstrations, presentations, critical thinking, and deduction. As a culminating assessment, students will solve right triangles in order to find out how tall the flagpole is in front of the school as well as how tall the school building is. 

Purpose/Essential Question(s): How do you solve right triangles? 

Time Frame: This lesson is designed for two ninety-minute class periods. 

Resources and Instructional Materials: 

Advanced Mathematical Concepts 
Glencoe/ McGraw-Hill 
936 Eastwind Drive 
Westerville, Ohio 43081-3329 
Pages 269-275 

Transparencies 

Overhead Projector

Poster Board

Protractors

String

Tape 

Straws 

Weights 

Tape Measures

Graph paper 

Calculator with trigonometric functions 



Day One 

Bell- Work: (work to be done when the student enters the class before the tardy bell) 

Have students copy the following trigonometric ratios off the overhead projector on a ready-made transparency: 

sino= opposite - csc 0 - hypotenuse hypotenuse opposite 
coso = adjacent - sec 0 hypotenuse hypotenuse adjacent 

tan 0 = -opposite Cot 0 adjacent adjacent opposite 

**Students can learn the major three: sin, cos, and tan, by memorizing one of the three mnemonic devices: 

1. SOH-CAH-TOA 

2. Some Old Horse Caught Another Horse Taking Oats Away 

3. Some Old Hippy Caught Another Hippy Tripping On Acid 

Motivating the lesson: 
Place the end of a yardstick at various heights along a stack of books on the floor to show students how the angle of elevation (the angle the yardstick make with the floor) changes with the height of the stack. Calculate the angle of elevation by using the height of the stack, the length of the yardstick, and the tangent ratio. 

Work through the following teacher-led examples: 
1. A right triangle has sides whose lengths are 3 cm, 4 cm, and 5 cm. Find the values of the six trigonometric functions of A. 

2. Solve right triangle ABC with m<A = 59 degrees, a = 8, and C is the right angle. Round angle measures to the nearest degree and side measures to the nearest tenth. 

3. In triangle PQR where Q is the right angle, p = 7, and q = 25, find the measure of <P to the nearest degree. 

4. The longest truck-mounted ladder used by the Dallas Fire Department is 120 feet long and consists of four hydraulic sections. An aerial expert for the fire department indicates that the optimal operating angle of this ladder is 60 degrees, allowing the ladder truck to be closer to buildings in the downtown streets of Dallas. Assuming the ladder is mounted 7 feet off the ground, how far from an 96-foot building should the base of the ladder be to achieve the optimal operating angle? How far should the ladder be extended to reach the room. 

Activity One: 
Have students work independently on Worksheet A for 15 minutes. Then let the students get with their partner (already selected by the teacher when designating collaborative pairs) compare work and reach a consensus on what the correct answers are. After another ten minutes, randomly select student pairs to come up and solve a right triangle on the overhead for the class to see. This assignment will be graded when the students turn in their work before their presentations by the following rubric: 

For homework, give the students some problems similar to those on Worksheet A.

Day Two 

Allow students to go over their homework problems by comparing answers with their partners. The teacher will ask for any questions and go over any problems the students may still be having trouble with. 

Activity Two 
Pair students with a partner. Students will receive Culminating Activity Sheet and the rubric for this lesson. In this activity, the students will demonstrate their ability to solve right triangle by finding: 

1. The height of the flagpole in front of the school 

2. The school building. 

The teacher will demonstrate how to use the protractor to measure the angle of elevation to the flagpole and to the top of the school building. The students will then follow the steps on the sheet in order to set up each of the right triangles on a poster board. The triangles will be drawn to scale and labeled correctly. The trigonometric ratios that they will use will be written on the poster board, as well as the calculations in order to solve the right triangle. The teacher will evaluate the culminating assessment with the following rubric: 

Worksheet A 
Solving Right Triangles 
(Click here for a printable Adobe Acrobat version)

Name _________________________________________________

Date _______________________________________

Solve each triangle described by drawing it like the one shown on the graph paper provided. Round angle measures to the nearest degree and side measures to the nearest tenth. 

9. Mrs. James is using a 7-meter ladder to clean the windows on her second floor. 
Her ladder stands on level ground and rests against the side of her house at a point 5 meters from the ground. How far from the side of the house is the foot of the ladder? 

10. .A hot air balloon rises at a rate of 80 feet per minute. An observer 450 feet from the place of ascent watches the balloon rise. What is the altitude of the balloon after 3 hours? 

Culminating Activity for 
Solving Right Triangles 
(Click here for a printable Adobe Acrobat version)

Name_________________________________________________

Materials Needed: Tape Measure, Poster Board, Protractor, Straw, String, Weight, Ruler, Calculator 

Procedures: 

1. Meet with your partner and decide who's going to do the measuring and who's going to do the recording. 

2. The partner that's recording, measure the measurer's height from the floor to their eye level. Record that here: ___________________________

3. Go out to the front of the school and measure of f a distance from the flagpole. Record that here: ______________________________

4. Take you protractor with the angle weight and measure the angle. Record that here: ___________________________ The angle you'll actually use will be 90degrees less. 

5. Now, measure off a distance from the side of the main building. Record that distance here: __________________________________

6. Measure the angle to the top of the building. Record that here: ________________
(Again, remember to subtract 90 degrees when solving your problem.) 

7. Now that all your measuring is done and we get back into the classroom, draw a scale model of the two objects we want to measure (the flagpole and the building). 

8. Use your knowledge of trigonometry to solve the right triangles and find the desired distances. 

**Make sure you put your name and your partner's name on the back of the poster! You'll be presenting these to the class, so be familiar with your results and how you got them.