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Answer:

Step-by-step explanation:

It is given that A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building, then let AC=14 foot and ∠C=45°and AB be the length of the building.

Thus, using the trigonometry, we have

[tex]\frac{AB}{AC}=sin45^{\circ}[/tex]

Substituting the given values, we get

⇒[tex]\frac{AB}{14}=\frac{1}{\sqrt{2}}[/tex]

⇒[tex]AB=14{\times}\frac{1}{\sqrt{2}}[/tex]

⇒[tex]AB=14{\times}\frac{\sqrt{2}}{2}[/tex]

⇒[tex]AB=7\sqrt{2} foot[/tex]

Thus, the length of the building will be [tex]7\sqrt{2} foot[/tex].

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The height up the building that the ladder reaches from the given parameters is; 7√2 ft

How to solve trigonometric ratios?

We are told that the length of the ladder is 14 ft.

Now, since the top of the ladder makes an angle of 45° with the building, then we can use trigonometric ratio to find how far the ladder rises up the building which is the vertical height.

Thus;

h/14 = sin 45

h = 14 sin 45

h = 14 * 1/√2

If we rationalize the denominator, we will have;

h = 7√2

Read more about trigonometric ratios at; https://brainly.com/question/13276558

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