Sara and Paul are on opposite sides of a building that a telephone pole fell on. The pole is leaning away from Paul at
an angle of 59° and towards Sara. Sara measures the angle of elevation to the top of the telephone pole to be 22°,
and Paul measures the angle of elevation to be 34°. Knowing that the telephone pole is about 35 ft. tall, answer the
following questions.
a. Draw a diagram of the situation.
b. How far apart are Sara and Paul?
c. If we assume the building is still standing, how tall is the building?

Question

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Respuesta :

dfbustos dfbustos · Answer 1 · 2020-01-12T23:57:59+01:00

Answer:

a) See figure attached

b) [tex] x = \frac{sin(124)}{sin(34)} 80.086 = 118.732 ft[/tex]

c) [tex] h = 35 sin (59) = 30.0 ft[/tex]

So then the heigth for the building is approximately 30 ft

Step-by-step explanation:

Part a

We can see the figure attached is a illustration for the problem on this case.

Part b

For this case we can use the sin law to find the value of r first like this:

[tex] \frac{sin(22)}{35 ft} =\frac{sin(59)}{r}[/tex]

[tex] r= \frac{sin(59)}{sin(22)} 35 ft = 80.086ft[/tex]

Then we can use the same law in order to find the valueof x liek this:

[tex] \frac{sin(124)}{x ft} =\frac{sin(34)}{80.086}[/tex]

[tex] x = \frac{sin(124)}{sin(34)} 80.086 = 118.732 ft[/tex]

And that represent the distance between Sara and Paul.

Part c

For this cas we are interested on the height h on the figure attached. We can use the sine indentity in order to find it.

[tex] sin (59) = \frac{h}{35}[/tex]

And if we solve for h we got:

[tex] h = 35 sin (59) = 30.0 ft[/tex]

So then the heigth for the building is approximately 30 ft