A boy 1.2m tall, stands 6m away from the foot of a vertical lamp pole 4.2m long if the lamp is at the tip of the pole
calculate the length of the shadow of the boy cast by the lamp
Angle of elevation of the lamp from the boy, correct to the nearest degree
maths
the lamp is 3m above the boy (4.2m - 1.2m)
the tangent of the angle of elevation from the top of the boy to the lamp
... tan(Θ) = 3m / 6m
length of shadow / boy's height = 6 / 3
Yes
Solve pls
To calculate the length of the shadow of the boy cast by the lamp, we can use similar triangles.
Let's set up the problem:
- Distance from the boy to the pole (h) = 6m
- Height of the pole (x) = 4.2m
- Height of the boy (y) = 1.2m
In the right triangle formed by the boy, the top of the pole, and its shadow, we have:
- The height of the pole (x) as the opposite side
- The distance from the boy to the pole (h) as the adjacent side
- The length of the boy's shadow (s) as the hypotenuse
- The height of the boy (y) as the corresponding side
Since we have similar triangles, we can set up a proportion to solve for the length of the shadow (s):
x/y = h/s
Substituting the given values:
4.2/1.2 = 6/s
Solving for s:
s = (6 * 1.2) / 4.2
s ≈ 1.714 m
Hence, the length of the shadow of the boy cast by the lamp is approximately 1.714 meters.
To solve for the angle of elevation of the lamp from the boy, we can use the inverse tangent function (tan^(-1)).
Let's set up the problem:
- The height of the pole (x) is the opposite side of the angle we want to find.
- The distance from the boy to the pole (h) is the adjacent side.
Using the tangent function:
tan(angle) = x/h
Substituting the given values:
tan(angle) = 4.2/6
Solving for the angle:
angle = tan^(-1)(4.2/6)
Using a calculator, the angle is approximately 35 degrees (to the nearest degree).
Hence, the angle of elevation of the lamp from the boy is approximately 35 degrees.