If a boy standing on the assembly ground looks at tje school flag from an angle of 32°and the length of the pole is 90cm.find the distance of the pole from the boy,to the nearest signifant figures using elevation and depression method
90 cm? That's some short pole.
Anyway, draw the triangle. The distance x to the pole can be found using
90/x = tan 32°
or
x/90 = tan 58°
To find the distance of the pole from the boy, we can use the trigonometric ratios of sine and cosine.
In this case, we will use the sine ratio as it involves the opposite side and the hypotenuse.
Let's assume that the distance of the pole from the boy is 'x'.
From the given information, we have:
- Angle of elevation (from the boy's eye level to the top of the pole): 32°
- Length of the pole (opposite side): 90 cm
Using the sine ratio:
sin(angle) = opposite/hypotenuse
sin(32°) = 90/x
To find 'x', we can rearrange the equation as follows:
x = 90 / sin(32°)
Using a calculator, we can evaluate the sin(32°) and then calculate 'x':
x ≈ 163.90 cm (to the nearest significant figures)
Therefore, the distance of the pole from the boy is approximately 163.90 cm.