A man 1.92 m tall, walking near a street light at night, casts a 3.88 m long shadow directly in front of him. The lightpost is 5.82 m behind the man. How tall is the lightpost?
Draw the figure. Note similar triangles. Let h be the height of the lamppost.
h/(5.82+3.88) = 1.92/3.88
check that on your figure.
To find the height of the lightpost, we need to use similar triangles.
Let's denote the height of the lightpost as 'x'.
According to the given information, the man's height is 1.92 m, and his shadow length is 3.88 m. The distance between the man and the lightpost is 5.82 m.
We can create a proportion using the corresponding sides of the similar triangles formed by the man, his shadow, and the lightpost. The corresponding sides are the man's height, his shadow length, and the distance between him and the lightpost.
The proportion can be written as:
(man's height) / (man's shadow length) = (distance between man and lightpost) / (height of lightpost)
Plugging in the values, we get:
1.92 m / 3.88 m = 5.82 m / x
We can cross-multiply and solve for 'x':
1.92 m * x = 3.88 m * 5.82 m
x = (3.88 m * 5.82 m) / 1.92 m
x ≈ 11.81 m
Therefore, the height of the lightpost is approximately 11.81 meters.