174 Trigonometry Applications PDF

# APPLICATIONS of 174 TRIGONOMETRY ## What you build? - A modern clinometer (Theodolite) to find heights of buildings. ## What you learn? - Heights and distances: Angle of elevation and angle of depression. ## What it improves? - Conceptual understanding - Hands-on skills - Innovation ## Learnin...

# APPLICATIONS of 174 TRIGONOMETRY ## What you build? - A modern clinometer (Theodolite) to find heights of buildings. ## What you learn? - Heights and distances: Angle of elevation and angle of depression. ## What it improves? - Conceptual understanding - Hands-on skills - Innovation ## Learning by doing - Name: - Roll no: - Class: ## Kit components to do activities - A clinometer. - A ruler. - A protractor. - A measuring tape. - A spirit level. - A target. ## Table of Contents | Type | Time | Page No | |---|---|---| | Information | 5 min | 1 | | Activity | 15 min | 2 | | Activity | 15 min | 3 | | Activity | 20 min | 5 | | Self assessment | 15 min | 7 | | Activity | 5 min | 8 | | Self assessment | 10 min | 9 | | Total time | 85 min | | ## Where is Trigonometry used? - Designing eye-glass lenses. - Controlling robotic arms and legs. - Constructing roads and buildings. - Producing medical scans. - Many other areas. ## Line of sight: - A straight line drawn from the eye of the observer to the point that the observer is viewing. ## Angle of elevation: - The angle between the line of sight and the horizontal. - It is valid when the point being viewed is ABOVE the horizontal level. ## Angle of depression: - The angle between the line of sight and the horizontal. - It is valid only when the point being viewed is BELOW the horizontal level. ## Activity 1: Angle of elevation and depression - **Making the setup**: - An illustration of how to assemble the equipment for the activity. - There are 7 steps to assemble the equipment. ## Activity 2: Heights and distances - A diagram showing how to change the distance from the object being measured. - A table with 4 columns and 12 rows. - **Angle of stick** - **Distance (Adjacent)** - **Height from horizontal (Opposite)** - **Tanθ(Opposite/Adjacent)** - **Space for calculation** ## Activity 3: Theodolite - **Material**: - An illustration of the equipment needed to assemble the Theodolite. - Instructions on how to make a spirit level. ## Measuring the height of a tall object - **Instructions**: 1. Choose something tall to measure. 2. Determine your distance from the base of the object. 3. Look at the top of the object through your clinometer and determine the angle. 4. Calculate the height of the object using trigonometric functions. - **Space for calculation** ## Do it yourself: - Find the height of a tree using trigonometric ratios. - Look through the clinometer and find the angle of elevation of the top of the tree and angle of depression of the bottom of the tree. - Compute the height of the tree. - **Formula**: Height of tree = A+B - A = CxTan(a) - B = CxTan(b) ## Self assessment 1. Ajay wants to reach the top of a pole using a ladder of length 20 feet. He started climbing the ladder and when he reached exactly half the length of the ladder he is at a height of 6 feet from the ground. What do you think is the height of the pole? - (a) 12 - (b) 13 - (c) 14 - (d) 15 2. There is a tree which is at a distance of 60 meters from the observer. if the angle of elevation of the top of a tree is 45°, then the height of the tree could be: - (a) 120 - (b) 240 - (c) 180 - (d) 60 3. A person standing on the top of a building is viewing a person on the road. By observing the figure, can you guess the angle of depression? - (a) 30 - (b) 60 - (c) 55 - (d) 45 4. Abhishek is standing in front of a tree and observing the top of it. Which of the following is a true statement regarding the angle of elevation, A? - (a) A increases as he goes away from the tree - (b) A decreases as he goes near to the tree - (c) A increases as he goes near to the tree - (d) A will always remain constant 5. A tree is broken by a wind; its upper part touches the ground at a point 10 meters from the foot of the tree and makes an angle of 45° with the ground. The entire length of the tree is: - (a) 15 - (b) 20 - (c) 10(1 + √2) - (d) 10(1 + √3/2) 6. If both rabbits start running with the same speed, who will reach the tower first? - (a) Rabbit, A - (b) Rabbit, B - (c) Both reach at the same time - (d) Cannot be said 7. If Rabbit B travels a distance of 100m to reach the tower, the height of the tower is? - (a) 100m - (b) 60m - (c) 45m - (d) 105m 8. A 1.5m tall boy is standing at some distance from a 30m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building. - (a) 28.5√ 3 m - (b) 9.5√3 m - (c) 19√ 3 m - (d) 30m ## Check out other Science Projects @www.butterflyfields.com ## Climb Up The Innovation Ladder!! - **KEEDA** - **Self learner** - **TINKERER** - **DISCOVERER** - **INNOVATOR** - **SUPREMELY GIFTED** ## Higher the band, better the skill & capability ## Where are our ex-students? - Kinnera Priya - now in IIT Roorkee - 2007-10 - Akshar Yadavalli - got admission for B.S from all IVY League colleges in USA - 2008-12 - Rohan Aloor - now in Jindal Law School - 2007-09 ## Watch hundreads of project instruction videos at: - /TheButterflyfields ## Check out innovative project ideas at: - f/ButterflyFieldsIndia ## Students in these towns are now learning by doing! - Adilabad; Ahmedabad; Ambikapur; Armoor; Bangalore; Baroda; Bellare; Bhavnagar; Bijapur; Chanduluru; Chennai; Coimbatore; Cuddalore; Dharwad; Duliajan; Gangavaram; Gulbarga; Guntur; Guwahati; Honnutagi; Hosur; Hyderabad; Kanpur; Karur; Kodagu; Kolkatta; Kothur; Krishnagiri; Kurnool Dist; Madurai; Mahbubnagar; Morpi; Mumbai; Mysore; Nagpur; Narsaraopet; Nellore; Nizamabad; Noida; Nuzellapalli; Ooty; Paloncha; Pamidipadu; Panguluru; Pollachi; Pune; Ranebennur; Redlawada; Sandur; Sarapaka; Shimoga; Surat; Thane; Thanjavur; Thiruchengode; Tirupathi; Tumkur; Vijayawada; Visakhapatnam; Wadlakonda; Warangal; West Godavari; Zaheerabad. ## Help Line: +91-40-27711020. ## [email protected]