Jonathan walks up stairs that are inclined at 25 degrees to the horizontal and 10m long.
A.How far has he moved vertically?
B.How far has he moved horizontally?
A. h = 10*sin25o.
B. d = 10*Cos25.
To find out how far Jonathan has moved vertically and horizontally, we can use trigonometry.
A. How far has he moved vertically?
To find this, we need to calculate the vertical component of the displacement. We can use the sine function, which relates the ratio of the opposite side to the hypotenuse of a right triangle (in this case, the angle of inclination is 25 degrees).
sin(25 degrees) = opposite/hypotenuse
sin(25 degrees) = vertical distance/10m
Rearranging the equation, we get:
vertical distance = sin(25 degrees) * 10m
Using a calculator, we can compute the value of sin(25 degrees) to be approximately 0.4226. Thus, the vertical distance Jonathan has moved is:
vertical distance = 0.4226 * 10m
vertical distance ≈ 4.226m
Therefore, Jonathan has moved vertically approximately 4.226 meters.
B. How far has he moved horizontally?
To find this, we need to calculate the horizontal component of the displacement. We can use the cosine function, which relates the ratio of the adjacent side to the hypotenuse of a right triangle (again, in this case, the angle of inclination is 25 degrees).
cos(25 degrees) = adjacent/hypotenuse
cos(25 degrees) = horizontal distance/10m
Rearranging the equation, we get:
horizontal distance = cos(25 degrees) * 10m
Using a calculator, we can compute the value of cos(25 degrees) to be approximately 0.9063. Thus, the horizontal distance Jonathan has moved is:
horizontal distance = 0.9063 * 10m
horizontal distance ≈ 9.063m
Therefore, Jonathan has moved horizontally approximately 9.063 meters.