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A lamppost, CAB, bent at point A after a storm. The tip of the lamppost touched the ground at point C, as shown below:


What is the height, in feet, of the portion AB of the lamppost?


A. 14 over cos 60 degrees


B. 14 tan 60 degrees


C. 14 over tan 60 degrees


D. 14 cos 60 degrees

Respuesta :

abidemiokin

Answer:

14 tan 60 degrees

Step-by-step explanation:

Find the diagram attached

The diagram is a right triangle with the following features;

Opposite side = AB

Adjacent side = BC = 14

angle of elevation θ = 60°

According to SOH CAH TOA identity;

tan θ = opposite/adjacent

Substitute the given values

tan60 = AB/BC

tan60 = AB/14

Cross multiply

AB = 14tan60

Hence the height in feet of the portion AB of the lamppost is 14 tan 60 degrees

Ver imagen abidemiokin

The height of AB of the lamppost can be calculated using trigonometric ratio.

Since the lamppost bent over at an angle 60 degrees. The length of AB is 14tan60.

Trigonometric Ratio

This is the use of trigonometric ratios to solve problems in a right angle triangle where you have a side and an angle.

Data;

  • BC = 14
  • angle = 60 degree
  • AB = ?

To solve for AB, we can easily use the tangent of the angle

[tex]tan\theta = \frac{opposite}{adjacent}[/tex]

Let's substitute the values into the equation and proceed to solve

[tex]tan 60 = \frac{AB}{14}\\AB = 14tan60[/tex]

The length of AB is 14tan60.

Learn more trigonometric ratio here;

https://brainly.com/question/11967894

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