A person is 40 meters away from a hill. If the angle of elevation to the top of

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Question: A person is 40 meters away from a hill. If the angle of elevation to the top of the hill is 30 degrees, what is the height of the hill?

Options:

Correct Answer: 20√3 meters

Solution:

Height = distance * tan(30) = 40 * (1/√3) = 40/√3 = 20√3 meters.

A person is 40 meters away from a hill. If the angle of elevation to the top of the hill is 30 degrees, what is the height of the hill?

A person is 40 meters away from a hill. If the angle of elevation to the top of the hill is 30 degrees, what is the height of the hill?

Step 1: Understand the problem. You have a person standing 40 meters away from a hill and looking up at the top of the hill at an angle of 30 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the hill, the other side is the distance from the person to the base of the hill (40 meters), and the angle between the ground and the line of sight 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 person to the hill). So, tan(30 degrees) = height / 40 meters.
Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 5: Set up the equation. Now, you can write the equation: height = 40 * tan(30 degrees).
Step 6: Substitute the value of tan(30 degrees) into the equation. This gives you height = 40 * (1/√3).
Step 7: Simplify the equation. This means height = 40/√3.
Step 8: To make it easier to understand, you can multiply the numerator and denominator by √3. This gives you height = (40√3)/3.
Step 9: Calculate the height. The final height of the hill is approximately 20√3 meters.

Trigonometry – The problem tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
Right Triangle Properties – The question involves applying properties of right triangles to find the height of the hill using the given distance and angle.