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Worksheet
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 - Practice Worksheet
Strengthen your foundation with key concepts and basic applications.
This worksheet covers essential long-answer questions to help you build confidence in Some Applications of Trigonometry from Mathematics for Class X (Mathematics).
Questions
Explain the concept of angle of elevation and angle of depression with real-life examples.
Think about how you look at objects above or below your eye level and the angle your line of sight makes with the horizontal.
A tower stands vertically on the ground. From a point on the ground, 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.
Use the tangent ratio for the angle of elevation to relate the height of the tower and the distance from the point to the tower.
An electrician needs to reach a point 1.3 m below the top of a 5 m tall pole to repair an electric fault. She uses a ladder inclined at an angle of 60° to the horizontal. Find the length of the ladder and how far from the foot of the pole she should place the foot of the ladder.
Consider the ladder as the hypotenuse of a right triangle and use trigonometric ratios to find the unknown sides.
From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed on a 20 m high building are 45° and 60° respectively. Find the height of the transmission tower.
Use the tangent of the angles of elevation to set up equations relating the heights and the distance from the point to the building.
The shadow of a tower standing on level ground is found to be 40 m longer when the sun's altitude is 30° than when it is 60°. Find the height of the tower.
Set up equations using the tangent of the sun's altitude angles and solve for the height of the tower.
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming there is no slack in the string.
Use the sine ratio for the angle of inclination to relate the height of the kite and the length of the string.
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Use the tangent of the angles of elevation and depression to find the height of the tower relative to the building.
Two poles of equal heights are standing opposite each other on either side of a road 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°. Find the height of the poles and the distances of the point from the poles.
Set up equations using the tangent of the angles of elevation and solve for the height and distances.
A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.
Use the tangent of the angles of elevation from both points to set up equations and solve for the height and width.
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
Use the tangent of the angles of depression to relate the height of the tower and the distances, and consider the uniform speed of the car to find the time.
Some Applications of Trigonometry - Mastery Worksheet
Advance your understanding through integrative and tricky questions.
This worksheet challenges you with deeper, multi-concept long-answer questions from Some Applications of Trigonometry to prepare for higher-weightage questions in Class X.
Questions
A tower stands vertically on the ground. From a point on the ground, 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.
Remember that tan(θ) = opposite/adjacent in a right-angled triangle.
An electrician needs to reach a point 1.3 m below the top of a 5 m tall pole to repair an electric fault. She uses a ladder inclined at an angle of 60° to the horizontal. Find the length of the ladder and how far from the foot of the pole she should place the ladder.
Break the problem into finding the ladder's length first, then its horizontal distance from the pole.
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
First find the distance to the building using the angle of elevation to its bottom, then use that to find the tower's height.
A statue stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and of the top of the pedestal is 45°. If the statue is 1.6 m tall, find the height of the pedestal.
Use the angle to the pedestal to express distance in terms of h, then apply the angle to the statue.
Two poles of equal heights stand opposite each other on either side of an 80 m wide road. From a point between them on the road, the angles of elevation of the tops are 60° and 30°. Find the height of the poles and the distances of the point from the poles.
Set up equations for each angle of elevation and solve the system for x and h.
From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
Use the angle of depression to find the distance to the tower, then the angle of elevation to find its height.
A 1.2 m tall girl spots a balloon at an angle of elevation of 60°. After some time, the angle reduces to 30°. Find the distance travelled by the balloon if its height is 88.2 m from the ground.
Calculate horizontal distances at both angles and find the difference.
A man observes a car at an angle of depression of 30°, which is approaching the foot of a tower. Six seconds later, the angle is 60°. Find the time taken by the car to reach the foot of the tower from the second observation.
Express distances in terms of h, find speed, then time to cover the remaining distance.
Compare and contrast the concepts of angle of elevation and angle of depression with examples.
Focus on the direction of the line of sight relative to the horizontal.
Explain how trigonometric ratios can be used to determine the height of an object without directly measuring it, using an example.
Think about forming a right triangle with the object and using known angle and distance.
Some Applications of Trigonometry - Challenge Worksheet
Push your limits with complex, exam-level long-form questions.
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Some Applications of Trigonometry in Class X.
Questions
A tower stands vertically on the ground. From a point on the ground, 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower. Justify your method of calculation.
Consider which trigonometric ratio relates the angle of elevation to the opposite side (height) and the adjacent side (distance from the tower).
An electrician needs to reach a point 1.3 m below the top of a 5 m tall pole to repair an electric fault. She uses a ladder inclined at 60° to the horizontal. Calculate the length of the ladder and how far from the pole she should place its foot.
Break the problem into finding the ladder's length first, then use another trigonometric ratio to find the distance from the pole.
From a point on the ground, the angle of elevation of the top of a building is 30° and the angle of elevation of the top of a flagstaff on the building is 45°. The building is 10 m tall. Find the height of the flagstaff and the distance from the point to the building.
First find the distance using the building's height and the angle of elevation to its top, then use the 45° angle to find the total height including the flagstaff.
The shadow of a tower on level ground is 40 m longer when the sun's altitude is 30° than when it is 60°. Find the height of the tower.
Set up two equations based on the two angles and solve for the unknowns.
From the top of a multi-storeyed building, the angles of depression of the top and bottom of an 8 m tall building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings.
Use the angles of depression to relate the heights and distances, remembering that the angle of depression equals the angle of elevation from the lower point.
A bridge is 3 m above a river. From a point on the bridge, the angles of depression of the banks on opposite sides are 30° and 45°. Find the width of the river.
Calculate the distances to each bank separately and add them together to get the total width.
A circus artist is climbing a 20 m long rope tied from the top of a vertical pole to the ground. If the angle between the rope and the ground is 30°, find the height of the pole.
The rope acts as the hypotenuse of a right-angled triangle, with the pole as the opposite side to the angle.
A tree breaks and the top touches the ground 8 m from the base, making a 30° angle. Find the original height of the tree.
The broken part forms a right-angled triangle with the ground and the remaining part of the tree.
Two slides in a park are for different age groups. One is 1.5 m high at 30° inclination, and the other is 3 m high at 60°. Find the lengths of both slides.
The slide length is the hypotenuse of a right-angled triangle where the height is the opposite side to the angle of inclination.
A kite is flying at 60 m height with the string making a 60° angle with the ground. Find the length of the string assuming no slack.
Use the sine of the angle to relate the height to the string length.
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.
