Question

AYUDA, POR FAVOR, URGENTÍSIMO. Desde un muro de 6m de altura se observa la parte alta y baja de un poste de luz con ángulos de elevación y depresión de 60 y 30 grados respectivamente. Determine la altura del poste.

Answer 1

To determine the height of the post, we can use trigonometry and set up two right triangles based on the given angles. By setting up equations using the tangent function and solving for the height, we find that the height of the post is 6 * √3/√3 - 1.

Step-by-step explanation:

To solve this problem, we can use trigonometry. Let's start by drawing a diagram:

Let h be the height of the post and d be the distance from the base of the post to the wall.

From the information given, we know that the angle of elevation from the top of the wall to the top of the post is 60 degrees and the angle of depression from the bottom of the wall to the bottom of the post is 30 degrees.

We can set up two right triangles to represent the situation:

- The triangle with the top of the wall, the top of the post, and the base of the post has a height of h and a base of d.

- The triangle with the bottom of the wall, the bottom of the post, and the base of the post has a height of h - 6 (the difference in height between the top and bottom).

Using the tangent function, we can set up the following equations:

tan(60) = h/d

tan(30) = (h - 6)/d

Simplifying these equations:

d = h/tan(60)

d = (h - 6)/tan(30)

Now we can set these two equations equal to each other and solve for h:

h/tan(60) = (h - 6)/tan(30)

After solving this equation, we find that h = 6 * √3/√3 - 1