If the angle of elevation from a point 50 meters away from the base of a hill is

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

Options:

Correct Answer: 25 meters

Solution:

Using tan(30) = height/50, height = 50 * (1/√3) = 50/√3 = 25 meters.

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

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

Step 1: Understand the problem. We have a hill and we are looking for its height. We are standing 50 meters away from the base of the hill.
Step 2: Identify the angle of elevation. The angle of elevation from our point to the top of the hill is 30 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the hill) divided by the adjacent side (distance from the base).
Step 4: Write the equation using the tangent function. We have tan(30 degrees) = height / 50 meters.
Step 5: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 6: Substitute the value of tan(30 degrees) into the equation. So, we have 1/√3 = height / 50.
Step 7: Solve for height. Multiply both sides by 50 to get height = 50 * (1/√3).
Step 8: Simplify the equation. This gives us height = 50/√3.
Step 9: Calculate the height. To find the numerical value, we can approximate 50/√3, which is about 25 meters.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the hill and the distance from the base.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the hill, the distance from the point to the base, and the angle of elevation.