From a point on the ground, the angle of elevation to the top of a hill is 30 de

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Question: From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

Options:

100√3 m
50 m
100 m
50√3 m

Correct Answer: 50 m

Solution:

Using tan(30°) = height/distance, we have height = distance * tan(30°) = 100 * (1/√3) = 100/√3 = 50 m.

From a point on the ground, the angle of elevation to the top of a hill is 30 de

Practice Questions

From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

100√3 m
50 m
100 m
50√3 m

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?

Step 1: Understand that the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the hill.
Step 2: Identify the distance from the point on the ground to the base of the hill, which is given as 100 meters.
Step 3: Recognize that we can use the tangent function (tan) to find the height of the hill. The formula is: tan(angle) = height / distance.
Step 4: Substitute the known values into the formula. Here, the angle is 30 degrees and the distance is 100 meters: tan(30°) = height / 100.
Step 5: Calculate tan(30°). The value of tan(30°) is 1/√3.
Step 6: Rewrite the equation using the value of tan(30°): 1/√3 = height / 100.
Step 7: To find the height, multiply both sides of the equation by 100: height = 100 * (1/√3).
Step 8: Simplify the expression: height = 100/√3.
Step 9: To get a numerical value, you can approximate 100/√3, which is about 57.74 meters, but the exact height is 100/√3.

Trigonometry – The problem tests the understanding of basic trigonometric functions, specifically the tangent function, which relates angles to opposite and adjacent sides in a right triangle.
Angle of Elevation – The question involves interpreting the angle of elevation from a point on the ground to the top of a hill, which is a common application of trigonometry in real-world scenarios.
Right Triangle Properties – The problem requires knowledge of the properties of right triangles, where the height of the hill represents the opposite side and the distance to the base represents the adjacent side.

From a point on the ground, the angle of elevation to the top of a hill is 30 de

What’s inside this PDF?

From a point on the ground, the angle of elevation to the top of a hill is 30 de

Practice Questions

Questions & Step-by-Step Solutions

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