Explore real-world applications of trigonometry in measuring heights, distances, and angles in various fields such as astronomy, navigation, and architecture.
Some Applications of Trigonometry - Quick Look Revision Guide
Your 1-page summary of the most exam-relevant takeaways from Mathematics.
This compact guide covers 20 must-know concepts from Some Applications of Trigonometry aligned with Class X preparation for Mathematics. Ideal for last-minute revision or daily review.
Complete study summary
Essential formulas, key terms, and important concepts for quick reference and revision.
Key Points
Define angle of elevation.
The angle of elevation is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level. For example, looking up at a tower from the ground.
Define angle of depression.
The angle of depression is the angle formed by the line of sight with the horizontal when the point being viewed is below the horizontal level. For example, looking down at a flower pot from a balcony.
Use tan to find height.
When the angle of elevation and distance from the object are known, use tan(θ) = opposite/adjacent to find the height. Example: tan(60°) = height/distance.
Use sin to find hypotenuse.
When the angle and opposite side are known, use sin(θ) = opposite/hypotenuse to find the hypotenuse. Example: finding ladder length.
Use cos to find adjacent side.
When the angle and hypotenuse are known, use cos(θ) = adjacent/hypotenuse to find the adjacent side. Example: finding distance from a point.
Real-world application: tower height.
Trigonometry is used to find the height of towers or buildings without direct measurement, using angles of elevation and distances.
Real-world application: ladder placement.
Determining the correct length and placement of a ladder using angles and heights to ensure safety and reach.
Misconception: angle of elevation vs depression.
Confusing angle of elevation with depression. Remember, elevation is looking up; depression is looking down.
Formula: tan(θ) = opposite/adjacent.
Key formula for right-angled triangles to find the opposite side when the angle and adjacent side are known.
Formula: sin(θ) = opposite/hypotenuse.
Key formula for right-angled triangles to find the hypotenuse when the angle and opposite side are known.
Formula: cos(θ) = adjacent/hypotenuse.
Key formula for right-angled triangles to find the adjacent side when the angle and hypotenuse are known.
Example: finding chimney height.
Given the angle of elevation and observer's height, calculate the chimney's height using tan(θ).
Example: flagstaff length.
Determine the length of a flagstaff on a building using two angles of elevation from a point.
Shadow length problems.
Solve for object height using shadow length changes with varying sun angles, applying tan(θ).
Multi-storeyed building height.
Calculate the height of a multi-storeyed building using angles of depression and basic trigonometry.
River width calculation.
Determine the width of a river using angles of depression from a bridge and the height of the bridge.
Memory hack: SOHCAHTOA.
Remember SOHCAHTOA for sin, cos, tan definitions: Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent.
Frequently tested: angle applications.
Exam questions often involve applying angles of elevation and depression to real-world scenarios like towers, ladders, and shadows.
Important diagram: right triangle.
Always draw a right triangle to visualize the problem, labeling the opposite, adjacent, and hypotenuse sides relative to the angle.
Practice problem: kite string length.
Given the kite's height and angle of elevation, use sin(θ) to find the length of the string.
Explore the world of quadratic equations, learning to solve them using various methods like factoring, completing the square, and the quadratic formula.
A chapter that explores sequences where each term after the first is obtained by adding a constant difference, focusing on their properties, nth term, and sum formulas.
Explore the properties, types, and theorems related to triangles, including congruence and similarity, to solve geometric problems effectively.
Coordinate Geometry explores the relationship between algebra and geometry through the use of coordinate systems to represent geometric shapes and solve problems.
Explore the basics of trigonometry, including angles, triangles, and the fundamental trigonometric ratios: sine, cosine, and tangent.
