Right Angled Triangles And Pythagoras Property

To solve the problem, we need to determine the length of the wire connecting the tops of two poles, given their heights and the angle the wire makes with the horizontal. Let us analyze this step by step.

1. Understanding the Problem:
The tops of two poles are at heights of and . The wire connecting these tops makes an angle of with the horizontal. We need to find the length of the wire.

2. Key Observations:
The difference in height between the two poles is:

$ , and the wire is the hypotenuse. Using the sine function, we have:

\) , we can write:

\) . Then:

\) :

\) $

4. Conclusion:
The length of the wire is .

Final Answer:
The correct option is .

To solve the problem, we need to find the angle of elevation of the top of a tower from a point 100 m away from the base, given that the height of the tower is also 100 m.

1. Understanding the Right Triangle Setup:
In this scenario:

• Height of the tower (opposite side) = 100 m
• Distance from the point to the base of the tower (adjacent side) = 100 m

Let the angle of elevation be . Then:

2. Solving for the Angle:
We know: So,

Final Answer:
The angle of elevation is 45° (Option D).