If the angle of elevation from a point 50 meters away from the base of a tower i

₹0.0

Question: If the angle of elevation from a point 50 meters away from the base of a tower is 30 degrees, what is the height of the tower?

Options:

Correct Answer: 25 meters

Solution:

Let h be the height of the tower. tan(30°) = h/50. Therefore, h = 50 * tan(30°) = 50 * (1/√3) = 50/√3 = 25√3/3 meters.

If the angle of elevation from a point 50 meters away from the base of a tower is 30 degrees, what is the height of the tower?

If the angle of elevation from a point 50 meters away from the base of a tower is 30 degrees, what is the height of the tower?

Step 1: Understand the problem. We have a tower and a point 50 meters away from its base. We need to find the height of the tower using the angle of elevation, which is 30 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the tower (h), the other side is the distance from the point to the base of the tower (50 meters), and the angle between the ground and the line of sight to the top of the tower is 30 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the tower) divided by the adjacent side (distance from the point to the base). So, tan(30°) = h / 50.
Step 4: Rearrange the equation to solve for h. Multiply both sides by 50: h = 50 * tan(30°).
Step 5: Find the value of tan(30°). The value of tan(30°) is 1/√3.
Step 6: Substitute the value of tan(30°) into the equation: h = 50 * (1/√3).
Step 7: Simplify the equation: h = 50/√3.
Step 8: To make it easier to understand, multiply the numerator and denominator by √3: h = (50√3)/(3).
Step 9: The final height of the tower is 25√3/3 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the point of observation.
Angle of Elevation – Understanding the concept of angle of elevation is crucial for setting up the right triangle in the problem.
Right Triangle Properties – The relationship between the sides of a right triangle and the angles formed is essential for solving the problem.