A man is standing at a distance of 50 m from a tower. The angle of elevation of
Practice Questions
Q1
A man is standing at a distance of 50 m from a tower. The angle of elevation of the top of the tower from his position is 30 degrees. Find the height of the tower. (2021)
25 m
15 m
20 m
10 m
Questions & Step-by-Step Solutions
A man is standing at a distance of 50 m from a tower. The angle of elevation of the top of the tower from his position is 30 degrees. Find the height of the tower. (2021)
Step 1: Understand the problem. A man is standing 50 meters away from a tower and looking up at the top of the tower at an angle of 30 degrees.
Step 2: Identify the right triangle formed by the man, the top of the tower, and the base of the tower. The distance from the man to the tower is the base of the triangle (50 m), and the height of the tower is the vertical side.
Step 3: Use the tangent function, which relates the angle of elevation to the opposite side (height of the tower) and the adjacent side (distance from the tower). The formula is: tan(angle) = opposite/adjacent.
Step 4: Plug in the values into the formula. Here, the angle is 30 degrees, the opposite side is the height of the tower (let's call it 'h'), and the adjacent side is 50 m. So, tan(30) = h / 50.
Step 5: Calculate tan(30). The value of tan(30 degrees) is 1/√3.
Step 6: Set up the equation: 1/√3 = h / 50.
Step 7: Solve for 'h' by multiplying both sides by 50: h = 50 * (1/√3).
Step 8: Calculate the height: h = 50/√3, which is approximately 28.87 m.
Step 9: Round the height to the nearest whole number, which is 29 m.
Trigonometry – The problem tests the application of trigonometric ratios, specifically the tangent function, to find the height of a tower using the angle of elevation.
Angle of Elevation – Understanding the concept of angle of elevation and how it relates to the height and distance in right triangles.
Right Triangle Properties – Utilizing properties of right triangles to solve for unknown lengths using known angles and distances.
