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

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What’s inside this PDF?

Question: From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the distance from the point to the base of the hill is 10 meters, what is the height of the hill?

Options:

10 meters
5 meters
15 meters
20 meters

Correct Answer: 10 meters

Solution:

Using tan(45) = height/10, height = 10 * tan(45) = 10 meters.

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 distance from the point to the base of the hill is 10 meters, what is the height of the hill?

10 meters
5 meters
15 meters
20 meters

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 distance from the point to the base of the hill is 10 meters, what is the height of the hill?

Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from your point on the ground and the line of sight to the top of the hill.
Step 2: Identify that the angle of elevation is 45 degrees.
Step 3: Recognize that the distance from your point to the base of the hill is 10 meters.
Step 4: Use the tangent function, which relates the angle of elevation to the height of the hill and the distance from the point to the base of the hill. The formula is: tan(angle) = height / distance.
Step 5: Substitute the known values into the formula: tan(45 degrees) = height / 10 meters.
Step 6: Know that tan(45 degrees) equals 1. So, the equation becomes: 1 = height / 10 meters.
Step 7: Solve for height by multiplying both sides of the equation by 10 meters: height = 10 meters * 1.
Step 8: Conclude that the height of the hill is 10 meters.

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 line.
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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