contestada

An 8-foot rope is tied from the top of a pole to a stake in the ground,as shown in the diagram below.

If the rope a 57° angle with the ground, what is the height of the pole, to the nearest tenth of a foot?

A 4.4
B 6.7
C 9.5
D 12.3

Respuesta :

Hayyyy1
Answer = B
Hope this helps

The height of the pole, to the nearest tenth of a foot is given by: Option B: 6.7 feet

What is angle of elevation?

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

How to use right triangles to find the height of the specified pole?

Remember that we assume that pole is vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.

Referring to the attached figure below, we get:

  • Length of the rope = length of AC = |AC| = 8 feet
  • The angle of elevation of rope from ground: 57°

Using the tangent ratio, we get:

[tex]\sin(x) = \dfrac{\text{Length of perpendicular}}{\text{Length of hypotenuse}} = \dfrac{|AB|}{|AC|}\\\\|AB| = \sin(x) \times |AC|\\\\|AB| = \sin(57^\circ) \times 8 \approx 6.71 \approx 6.7\: \rm feet[/tex]

Thus, the length of the pole is approx 6.7 feet (option B).

Learn more about trigonometric ratios here:

https://brainly.com/question/22599614

Otras preguntas