A road worker holds a flag in position R with an out strech arm. He swings the flag downward and it forms angle of 30degrees with the ground P. His shoe Q is 2,5 away from P. His head is 24cm above his shoulder. calculate the height of the man
If R is at shoulder height, then the man's height is
.24 + 2.5 tan30° = 1.683 m
35
To calculate the height of the man, we can use basic trigonometry and the given information.
Let's break down the given information:
- The road worker swings the flag downward, forming an angle of 30 degrees with the ground at point P.
- His shoe, point Q, is 2.5 meters away from point P.
- The man's head is 24 centimeters (0.24 meters) above his shoulder.
Now let's calculate the height of the man step by step:
Step 1: Calculate the vertical distance from the ground to the flag at point P:
Since point P forms a right angle with the ground, we can use trigonometry to calculate this height. We can use the tangent function.
tan(30°) = (height of the flag at P) / 2.5 m
Rearranging the formula:
(height of the flag at P) = 2.5 m * tan(30°)
(height of the flag at P) = 2.5 m * 0.5774 (Approximately)
(height of the flag at P) = 1.4435 m (Approximately)
Step 2: Calculate the height of the man:
The height of the man is the sum of the height from point P to his shoulder and the height from his shoulder to his head.
The height from P to the man's shoulder = (height of the flag at P) + 0.24 m
The height of the man = (height from P to the man's shoulder) + 0.24 m
Substituting the values, we get:
height of the man = 1.4435 m + 0.24 m + 0.24 m
height of the man = 1.9235 m (Approximately)
Therefore, the height of the man is approximately 1.92 meters.