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PIT_PIT [208]
3 years ago
5

A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 31∘. he then moves back

57.1 feet and determines that the angle of elevation is 23.8∘. what is the height of the building?
Mathematics
2 answers:
atroni [7]3 years ago
6 0
<h2>Hello!</h2>

The answer is:

The height of the building is 94.29 feet.

<h2>Why?</h2>

To solve the problem, we need to consider that two triangles are formed depending on the distance where the surveyor is standing.

We have a first triangle which its base will be called "x" and its height will be called "h" with an angle of elevation from a point on the ground, equal to 31°.  

Also, we have a second triangle which base is equal to "x" + 57.1 feet, and a height "h", with an angle of elevation from a point on the ground, equal to 23.8°

We need to use a trigonometric identity that establishes a relationship between the height and the base. So, using the tangent trigonometric identity, we have:

Tan(\alpha)=\frac{Opposite}{Adjacent}

For the first triangle:

Tan(31\°)=\frac{h}{x}

0.60=\frac{h}{x}

h=0.60*x=0.60x

For the second triangle:

Tan(23.8\°)=\frac{h}{x+57.1feet}

0.44=\frac{h}{x+57.1feet}

(0.44)*(x+57.1feet)=h

h=0.44x+25.14feet

Then, making both equation equals, in order to find "x", we have:

0.60x=0.44x+25.14feet

0.60x-0.44x=25.14feet

0.16x=25.14feet

x=\frac{25.14feet}{0.16}=157.13feet

Then, we substituting "x" into any of the equations, we have:

Substituting into the first equation:

h=0.60*x\\\\h=0.60*(157.13feet)=94.29feet

Hence, the height of the building is 94.29 feet.

Have a nice day!

SVETLANKA909090 [29]3 years ago
3 0

Answer:

B and E

Step-by-step explanation: Because it is that on edge

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