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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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:
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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 .
