Analytic Geometry(Math)

a person 6 ft. tall s standing near a street light so that he is 4/10 of the distance from the pole to the tip of his shadow. How high above the ground is the light bulb? if the person's head is exactly 5ft from the light bulb. how far is the person from the pole and how long is the shadow?

  1. 👍
  2. 👎
  3. 👁
  1. as usual, draw a diagram.
    If the light is at height h, and the person is standing at a distance of 4x from the pole, then

    h/10x = 6/6x
    h/10 = 6/6
    h=10

    So, the light is 10 feet up.

    Now, if the person's head is 5' from the light,

    (4x)^2 + (10-6)^2 = 5^2
    (4x)^2 + 4^2 = 5^2

    We all know of the 3-4-5 right triangle, so 4x=3

    So, 6x = 4.5, and that is the length of the shadow.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    A street light is hung 18 ft. above street level. A 6-foot tall man standing directly under the light walks away at a rate of 3 ft/sec. How fast is the tip of the man's shadow moving? I know I would've to set up a proportion. 18 /

  2. Math

    Use similar triangle to solve. A person who is 6 feet tall standing 140 feet from the base of a tree and the tree casts a 150 foot shadow. The person's shadow is 10 feet in length. What is the height of the tree?

  3. English

    The speaker in "The Road Not Taken" is most clearly which type of person? A person who made a decision. A person who likes a well-beaten path. A person now standing at a fork. A person lost in the woods***

  4. Calculus

    A street light is mounted at the top of a 6 meter tall pole. A man 2m tall walks away from the top with a speed of 1.5 m/s along a straight path. How fast is the tip of his shadow moving when he is 10m from the pole?

  1. PHYSICS

    The observation deck of tall skyscraper 370 m above the street. Determine the time required for a penny to free fall from the deck to the street below.

  2. math

    Use similar triangles to solve. A person who is 5 feet tall is standing 117 feet from the base of a​ tree, and the tree casts a 130 foot shadow. The​ person's shadow is 13 feet in length. What is the height of the​ tree?

  3. Math

    A 6-foot person standing 15 feet from a streetlight casts a 10-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the

  4. Calculus

    A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is her shadow lengthening when she is 30 ft from the base of the pole?

  1. calculus

    A 5.5 foot tall woman walks at 6ft/s torward a street light that is 16.5 ft above the ground. what is the rate of change of the length of her shadow when she is 14ft from the street light? At what rate is the tip of her shadow

  2. Math

    A 6-foot person standing 15 feet from a streetlight casts a 15-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the

  3. Calculus

    A man 5.50 ft tall approaches a street light 18.0 ft above the ground at a rate of 4.0 ft/s. at what rate is the end of the man's shadow moving when he is 9.0 ft from the base of the light?

  4. Math

    Use similar triangles to solve. A person who is 6 feet tall is standing 108 feet from the base of a​ tree, and the tree casts a 120 foot shadow. The​ person's shadow is 12 feet in length. What is the height of the​ tree?

You can view more similar questions or ask a new question.