Aflagstaff is placed at one corner of rectangular field of 40m×30m. If angle of elevation of top of flagstaff is 30°.Find height flagstaff?
- PuzzlingLv 71 month ago
For a faster response, post this in Mathematics next time.
The distance along the diagonal is 50 m. You can show that using the Pythagorean Theorem or just using the fact that a 3-4-5 triangle is a right triangle.
Now draw the triangle formed by the diagonal (50 m) and a flag pole of height x. The angle is 30°.
We can use our knowledge of 30-60-90 triangles and the ratio of their sides:
short : hypotenuse : long = 1 : 2 : √3
In your triangle, the short leg is x and the long leg is 50.
short : long = x / 50
In the ratio:
short : long = 1 / √3
So set up an equation:
x / 50 = 1 / √3
Multiply both sides by 50
x = 50/√3
Rationalize the denominator:
x = (50√3)/3
x ≈ 28.9 m