a man 1.83m tall, stands at a distance of 14.8m away from the base of a tower. He discovers that the angle of elevation of the top of tower is 63. Calculate the height of the tower.
h1 = 1.83 m.
Tan63 = h2/14.8.
h2 = 14.8*Tan63 =
h = h1+h2 = ht. of tower.
I assume you mean that the angle of elevation is from the man's eye-level, or what does his height matter? Also, his eye-level can be approximated by his height.
If so, then draw a diagram, as always. Then check your basic trig functions. It should be clear that the desired height h can be found using
(h-1.83)/14.8 = tan63°
To calculate the height of the tower, we can use trigonometry.
Based on the information provided, we have a right-angled triangle formed by the man, the top of the tower, and the base of the tower.
The opposite side of the triangle is the height of the tower, and the adjacent side is the distance from the base of the tower to the man.
We can use the tangent function (tan) to find the height of the tower.
The formula for tangent is:
tan(angle) = opposite / adjacent
In this case, the angle of elevation is 63 degrees, the opposite side is the height of the tower, and the adjacent side is the distance from the base of the tower to the man.
Let's calculate the height of the tower:
tan(63) = opposite / 14.8
To solve for the opposite side (height), we rearrange the formula:
opposite = tan(63) * 14.8
Using a scientific calculator, we can find that:
opposite = 1.9 * 14.8 ≈ 28.12
Therefore, the height of the tower is approximately 28.12 meters.
To find the height of the tower, we can use trigonometry and specifically focus on the tangent function. Here's how you can calculate it step-by-step:
1. Draw a diagram: Sketch a right-angled triangle, representing the situation described in the problem. Label the height of the tower as 'h', the distance from the man to the base of the tower as 'd' (14.8m), and the angle of elevation as 'θ' (63 degrees). The vertical side of the triangle represents the height of the tower, while the horizontal side represents the distance from the man to the base of the tower.
2. Identify the trigonometric function: Since we want to find the height of the tower, which is the opposite side of the triangle to the angle of elevation, we can use the tangent function. The formula for tangent is:
tan(θ) = opposite / adjacent
3. Substitute known values: Substituting the known values into the formula, we get:
tan(63) = h / 14.8
4. Solve for 'h': Rearrange the equation to solve for 'h' by multiplying both sides by 14.8:
h = 14.8 * tan(63)
5. Calculate the height: Using a calculator, evaluate the right side of the equation to find the value of 'h':
h ≈ 14.8 * tan(63) ≈ 28.625
Therefore, the height of the tower is approximately 28.625 meters.