Answered

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A new building is being constructed a distance of 420 feet from the ocean, and the builder wants to have a rooftop patio

with a view of the ocean. Another building, in between the new building and the ocean, is located a distance of 180 feet

from the ocean and has a height of 15 feet. The angle of elevation from the ocean to the top of the new building, O.

represents the minimum angle for a person on the rooftop to view the edge of the ocean

rooftop

patio

15 ft.!

180 ft.

420 ft.

. To the nearest hundredth, what is the measure of in degrees?

. Construction for the new building has a maximum height restriction of 32 feet Is it possible for the builder to have a

rooftop patio with a view of the ocean? Justify your answer. In your response, make sure to define your variables

and show all your work

Enter your answers and justification in the box

Math symbols

Relations

No

Sagot :

MrRoyal

Answer:

[tex]\theta = 4.8^\circ[/tex]

It is possible

Step-by-step explanation:

Given

See attachment for the construction

Solving (a): The minimum angle

This is calculated as thus:

[tex]tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

[tex]tan(\theta) = \frac{15}{180}[/tex]

[tex]tan(\theta) = 0.0833[/tex]

Calculate [tex]\theta[/tex]

[tex]\theta = tan^{-1}(0.0833)[/tex]

[tex]\theta = 4.761[/tex]

[tex]\theta = 4.8^\circ[/tex] --- approximated

Solving (b):

First; calculate the height of the building using the following equivalent ratio.

[tex]h : 420 = 15 : 180[/tex]

Where h is the height of the building

[tex]\frac{h }{ 420 }= \frac{15 }{ 180}[/tex]

[tex]h= \frac{15 }{ 180}*420[/tex]

[tex]h= \frac{15*420 }{ 180}[/tex]

[tex]h= \frac{6300}{ 180}[/tex]

[tex]h= 35[/tex]

This means that it is possible that the builder builds a 32 feet high building

View image MrRoyal
  • Measure of angle θ will be 4.76°
  • It is not possible for the builder to have a rooftop patio with a view of the ocean.

Angle of depression:

  • Angle of depression is the angle formed between the horizontal line and the line of sight of the observer.

From the picture attached,

Angle of depression = Angle of elevation (θ)    [Alternate angles]

Apply tangent rule in ΔCDP,

[tex]\text{tan}\theta=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\text{tan}\theta=\frac{CD}{DP}[/tex]

       [tex]=\frac{15}{180}[/tex]

       [tex]=\frac{1}{12}[/tex]

[tex]\theta=\text{tan}^{-1}(0.08333)[/tex]

[tex]\theta=4.76^\circ[/tex]

Similarity of two triangles:

  • If two triangles are similar, their corresponding sides will be proportional.

Use this property to get the height of the new building.

Since, ΔABP and ΔCDP are the similar triangles, their corresponding sides will be proportional.

[tex]\frac{AB}{BP}=\frac{CD}{DP}[/tex]

[tex]\frac{AB}{420}=\frac{15}{180}[/tex]

AB = [tex]\frac{420\times 15}{180}[/tex]

     = 35 feet

But the construction for a new building has a maximum height restriction of 32 feet.

And the height of the building is more than the restricted height.

    Therefore, it is not possible for the builder to have a rooftop patio with a view of the ocean.

Learn more about the similar triangles here,

https://brainly.com/question/10043253?referrer=searchResults

View image eudora
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