A road-worker holds a flag in position R with an out stratched arm he swings the flag downwards and it forms an angle of 30 degree with the ground P.his shoe Q is 2,5 metre away from P.his head is 24 centimetre above his shoulder(s).calculate the height of the man.
To calculate the height of the man, we can break down the given information and use trigonometry.
1. From the information given, we can determine that we have a right triangle formed by the man's body. Let's label the different points and measurements:
- R: The position of the man's outstretched arm.
- P: The point where the flag swings downwards, forming a 30-degree angle with the ground.
- Q: The man's shoe, located 2.5 meters away from P.
- H: The man's head.
- S: The man's shoulder.
2. We are given that the man's head is 24 centimeters above his shoulder (S). Let's convert this measurement to meters since the other measurements are given in meters:
- Height of head above shoulder (SH) = 24 centimeters = 0.24 meters.
3. We need to determine the height of the man, which is the distance between the ground point P and the man's head point H.
4. Using trigonometry, we can focus on the right triangle formed by the points P, S, and H.
- The angle at P is 30 degrees.
- The side adjacent to the angle P is SQ, which has a length of 2.5 meters since the man's shoe is 2.5 meters away from P.
- The side opposite to the angle P is SH, which is the height of the man we need to calculate.
5. Since we have the lengths of the adjacent and opposite sides, we can use the tangent function to calculate the height SH:
- tan(angle P) = SH / SQ
Plugging in the values:
- tan(30 degrees) = SH / 2.5 meters
6. We can solve the equation for SH:
- SH = tan(30 degrees) * 2.5 meters
7. Finally, we calculate the value of SH:
- SH ≈ 1.44 meters.
So, the height of the man is approximately 1.44 meters.