To solve the problem, we need to find the value of using the properties of triangles and trigonometry.
1. Observing the Triangle Configuration: In the given figure, triangles and share angle , and angles (both marked as equal), which means the triangles are similar by AA similarity.
2. Using Property of Similar Triangles: From similar triangles , the corresponding sides are in proportion:
3. Substituting Given Values:
Let
Using similar triangles, we write:
4. Solving the Proportion:
, so:
Final Answer: The value of is .
03
PYQ 2025
medium
mathematicsID: ts-polyc
The angle of elevation of the top of the building from a point 10 meters away from the base of the building is 60°, then the height of the building is:
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3
4
Official Solution
Correct Option:
(2)
We are given that the distance from the point to the base of the building is 10 meters, and the angle of elevation to the top of the building is 60°. We need to find the height of the building. Step 1: Represent the situation in a right triangle. - The height of the building is the opposite side. - The distance from the point to the base of the building is the adjacent side. - The angle of elevation is . Step 2: Use the tangent of the angle of elevation to find the height : Step 3: We know that , so: Step 4: Solve for : Thus, the height of the building is .
04
PYQ 2025
medium
mathematicsID: ts-polyc
From the top of the tower 60 meters high, the angle of depression of an object is 60°, then the distance of the object from the base of the tower is:
1
2
3
4
Official Solution
Correct Option:
(1)
We are given that the height of the tower is 60 meters and the angle of depression is 60°. We need to find the distance of the object from the base of the tower. Step 1: Represent the situation in a right triangle. - The height of the tower (opposite side) is 60 meters. - The angle of depression is 60°, so the angle of elevation from the object to the top of the tower is also 60° (alternate angles). Step 2: Use the tangent of the angle of elevation to find the distance (adjacent side): Step 3: We know that , so: Step 4: Solve for : Thus, the distance of the object from the base of the tower is .
About Geometry - TS-POLYCET
Geometry is a vital chapter for TS-POLYCET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Geometry PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Geometry carry the most weight. Then, tackle the questions iteratively to solidify your understanding.
