From a point 30 meters away from the base of a tower, the angle of elevation to

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Question: From a point 30 meters away from the base of a tower, the angle of elevation to the top of the tower is 45 degrees. What is the height of the tower?

Options:

30 meters
45 meters
60 meters
15 meters

Correct Answer: 30 meters

Solution:

Using tan(45) = height / 30, we have height = 30 * tan(45) = 30 * 1 = 30 meters.

From a point 30 meters away from the base of a tower, the angle of elevation to

Practice Questions

From a point 30 meters away from the base of a tower, the angle of elevation to the top of the tower is 45 degrees. What is the height of the tower?

30 meters
45 meters
60 meters
15 meters

Questions & Step-by-Step Solutions

From a point 30 meters away from the base of a tower, the angle of elevation to the top of the tower is 45 degrees. What is the height of the tower?

Step 1: Understand the problem. You have a tower and you are standing 30 meters away from its base.
Step 2: The angle of elevation to the top of the tower is 45 degrees. This means if you draw a line from your eyes to the top of the tower, it makes a 45-degree angle with the ground.
Step 3: In a right triangle, the tangent of an angle is the ratio of the opposite side (height of the tower) to the adjacent side (distance from the tower).
Step 4: Write the formula for tangent: tan(angle) = opposite / adjacent. Here, tan(45) = height / 30.
Step 5: We know that tan(45 degrees) equals 1. So, we can write the equation as 1 = height / 30.
Step 6: To find the height, multiply both sides of the equation by 30: height = 30 * 1.
Step 7: Calculate the height: height = 30 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tower and the distance from the tower.
Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.

From a point 30 meters away from the base of a tower, the angle of elevation to

What’s inside this PDF?

From a point 30 meters away from the base of a tower, the angle of elevation to

Practice Questions

Questions & Step-by-Step Solutions

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