Word Problems Involving Right Triangles
- 1. WORD PROBLEMS INVOLVING RIGHT TRIANGLES By Rhea Ann N. Diaz
- 2. REVIEW 01 Please take out your scientific calculator.
- 3. Find the value of the following, correct to four decimal places. Sin 38° = 0.6157 Cos 75 ° = 0.2588 Tan 26 ° = 0.4877 Cos 54 ° = 0.5878 Tan 33 ° = 0.6494
- 4. Find the measure of the following angles to the nearest hundredths. A = 31.94 ° Sin A = 0.529 A = 𝒔𝒊𝒏−𝟏 𝟎. 𝟓𝟐𝟗 Cos B = 0.49 B = 𝒄𝒐𝒔−𝟏 𝟎. 𝟒𝟗 B = 60.66° Tan C = 1.8 C = 𝒕𝒂𝒏−𝟏𝟏. 𝟖 C = 60.95 ° Sin D = 0.256 D = 𝒔𝒊𝒏−𝟏𝟎. 𝟐𝟓𝟔 D = 14.83 ° Tan E = 0.7251 E = 𝒕𝒂𝒏−𝟏𝟎. 𝟕𝟐𝟓𝟏 E = 35.95 °
- 6. The Trigonometric River Your loved one lives on the other side of the river. Due to strict border protocol brought by pandemic, you cannot see each other just yet. You decided to send her a love letter through email. Because she’s an avid trigonometric fan, you wanted to impress her by applying trigonometry in your love letter. Thus, you wanted to solve the width of the river that separates you from her.
- 7. Let us Illustrate… On your side of the bank, you found a log that is 5 meters long, then using your protractor, you found that the angle between the end of the log and her side of the bank is 75° (as shown in the figure). Now solve for x which is the width of the river. 5 meters 75° x
- 8. Let us Process… 1 2 3 4 How will you solve for the width of the river? Is solving right triangles useful in everyday life? Were you able to apply the trigonometric ratios in solving for x in the right triangle? How? You are ready for today’s lesson!
- 9. PRESENTATION OF THE LESSON 03 And the learning begins…
- 10. —M9GE-Ive-1 At the end of the lesson, the students shall be able to use the trigonometric ratios to solve real-life problems involving right triangles. OBJECTIVE:
- 11. ACTIVITIES 04 A picture is worth a thousand words.
- 12. Solve for the width of the river. 5 m x 75° Solution: tan 𝜃 = 𝑜𝑝𝑝 𝑎𝑑𝑗 tan 75° = 𝑥 5 5 tan 75° = 𝑥 5 3.7321 = 𝑥 𝒙 = 𝟏𝟖. 𝟔𝟔 The width of the river is 18.66 meters.
- 13. Find the distance between the rock and the tower. 20 m x 31° Solution: tan 𝜃 = 𝑜𝑝𝑝 𝑎𝑑𝑗 tan 31° = 20 𝑥 𝑥 = 20 tan 31° 𝑥 = 20 0.6009 𝒙 = 𝟑𝟑. 𝟐𝟖 The distance between the rock and the tower is 33.28 meters.
- 14. Solve for ∠𝑨. 4 m 𝐴 Solution: tan 𝐴 = 𝑜𝑝𝑝 𝑎𝑑𝑗 tan 𝐴 = 4 7 tan 𝐴 = 0.5714 𝐴 = 𝑡𝑎𝑛−10.5714 𝑨 = 𝟐𝟗. 𝟕𝟒 The measure of ∠𝑨 is 29.74° 7 m
- 15. Let’s Level Up!
- 16. Draw and Solve! A ladder 6 meters long leans against the wall of a building. If the foot of the ladder makes an angle of 54° with the ground, how far is the base of the ladder from the wall?
- 17. Draw and Solve! A 5-meter ladder leans against the wall of a house. The foot of the ladder on the ground is 2.6 meters from the wall. What angle does the ladder make with the wall?
- 18. Draw and Solve! A girl who is on the second floor of their house watches her cat lying on the ground. The angle between her eye level and her line of sight is 36°. If the girl is 3 meters above the ground, approximately how far is the cat from the house?
- 19. ANALYSIS 05 Let’s see what you think!
- 20. Let’s answer these questions: How important is illustrating pictures in solving word problems involving right triangles? How did you use your knowledge on trigonometric ratios in solving problems involving right triangles?
- 22. What are the steps in solving real-life problems involving right triangles?
- 23. Steps in solving real-life problems involving right triangles: 1 2 3 4 Draw and label. Determine the formula (trigonometric ratio) to be used. Identify what are given and what is asked in the problem (opposite, adjacent or hypotenuse). Solve.
- 25. The Exodus Problem From point A, Moses walked 65 miles west then 58 miles north to his destination B. Find the angles made from his starting point to his destination and vice versa (∠𝐴 and ∠𝐵) and his displacement (c). A B c C
- 27. Illustrate the following problems then solve. 1. A ladder 6 meters long leans against the wall of a house. If the foot of the ladder makes an angle of 65° with the ground, how far is the base of the ladder from the wall? 2. Drake is flying a kite. He is holding the end of the string at a distance of 1.5 m above the ground. If the string is 18 m long and makes an angle of 42° with the horizontal, how high is the kite above the ground? 3. A 10-meter post was unearthed and leaned on the tree. The foot of the post is 4.6 meters from the base of the tree. What angle does the post make with the tree?
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