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Sofia leans a 28-foot ladder against a wall so that it forms an angle of 67° with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.​

Answer :

Using the slope concept, it is found that the ladder reaches a height of 65.96 feet.

What is a slope?

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

In this problem:

  • The vertical change is the height that we want to find.
  • The horizontal change is the ladder of 28 feet.
  • The angle is of 67º.

Hence:

[tex]\tan{67^\circ} = \frac{h}{28}[/tex]

[tex]h = 28\tan{67^\circ}[/tex]

[tex]h = 65.96[/tex]

The ladder reaches a height of 65.96 feet.

You can learn more about the slope concept at https://brainly.com/question/18090623

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