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A 12-foot pole is supporting a tent and has a rope attached to the top. The rope is pulled straight and the other end is attached to a
peg two foot above the ground. The rope and the pole form an angle that measures 40°, as shown below.
Which expression shows the length of the rope?

A 12foot pole is supporting a tent and has a rope attached to the top The rope is pulled straight and the other end is attached to a peg two foot above the grou class=

Respuesta :

The expression that shows the length of the rope is 10 / cos 40° = 13.1 feet

How to find the side of a right triangle?

The side of the right triangle can be found using trigonometric ratios.

Hence,

cos ∅ = adjacent / hypotenuse

where

adjacent side = 12  - 2 = 10 ft

hypotenuse side = rope length

∅ = 40°

Therefore,

cos ∅ = 10 / x

cos 40° = 10 / x

cross multiply

x cos 40° = 10

Therefore,

divide both sides by cos 40°

x cos 40° / cos 40° = 10 / cos 40°

x = 10 / cos 40°

x = 10 / 0.76604444311

x = 13.0548302872

x = 13.1 feet

The expression that shows the length of the rope is 10 / cos 40° = 13.1 feet

learn more on right triangle here: https://brainly.com/question/28050028

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