A tower is 100 meters high. From a point on the ground, the angle of elevation t
Practice Questions
Q1
A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
100√3 meters
50√3 meters
200 meters
150 meters
Questions & Step-by-Step Solutions
A tower is 100 meters high. From a point on the ground, the angle of elevation to the top of the tower is 30 degrees. How far is the point from the base of the tower?
Step 1: Understand the problem. We have a tower that is 100 meters high and we want to find out how far a point on the ground is from the base of the tower.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the tower is given as 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 tower) divided by the adjacent side (distance from the base).
Step 4: Write the formula. The formula we will use is: Distance = height / tan(angle).
Step 5: Substitute the values into the formula. Here, height = 100 meters and angle = 30 degrees. So, Distance = 100 / tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 7: Substitute tan(30 degrees) into the formula. Now we have Distance = 100 / (1/√3).
Step 8: Simplify the equation. Dividing by a fraction is the same as multiplying by its reciprocal, so Distance = 100 * √3.
Step 9: Final calculation. Therefore, the distance from the point to the base of the tower is 100√3 meters.
Trigonometry – The problem involves using the tangent function to relate the height of the tower to the distance from the base using the angle of elevation.
Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tower, the distance from the base, and the angle of elevation.
