From a point on the ground, the angle of elevation to the top of a hill is 45 de

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Question: From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 20 m, how far is the point from the base of the hill?

Options:

20 m
10 m
30 m
40 m

Correct Answer: 20 m

Solution:

Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.

From a point on the ground, the angle of elevation to the top of a hill is 45 de

Practice Questions

From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 20 m, how far is the point from the base of the hill?

20 m
10 m
30 m
40 m

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 20 m, how far is the point from the base of the hill?

Correct Answer: 20 m

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 that the height of the hill is 20 meters.
Step 3: Recognize that the angle of elevation is 45 degrees.
Step 4: Recall the tangent function in trigonometry, which is defined as tan(angle) = opposite/adjacent.
Step 5: In this scenario, the 'opposite' side is the height of the hill (20 m) and the 'adjacent' side is the distance from the point to the base of the hill.
Step 6: Set up the equation using the tangent of 45 degrees: tan(45°) = height/distance.
Step 7: Substitute the known values into the equation: tan(45°) = 20/distance.
Step 8: Since tan(45°) equals 1, rewrite the equation as 1 = 20/distance.
Step 9: Solve for distance by rearranging the equation: distance = 20 m.

Trigonometry – Understanding the relationship between angles and sides in right triangles, specifically using the tangent function.
Angle of Elevation – The angle formed by the line of sight from a point on the ground to the top of an object above the horizontal.
Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.

From a point on the ground, the angle of elevation to the top of a hill is 45 de

What’s inside this PDF?

From a point on the ground, the angle of elevation to the top of a hill is 45 de

Practice Questions

Questions & Step-by-Step Solutions

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