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belka [17]
2 years ago
11

(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in

the image safe?
(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.

Mathematics
2 answers:
Galina-37 [17]2 years ago
8 0

Find Q

  • tanQ=Perpendicular/Base
  • tanQ=4/15
  • tanQ=0.26
  • Q=tan^-¹(0.26)
  • Q=14.6°

Not safe

Apply Pythagorean theorem

PR²=4²+15²=16+225=241

  • PR=√241
mihalych1998 [28]2 years ago
3 0

Answer:

a) not safe

b) 15.5 ft (nearest tenth)

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

<u>Tan trig ratio</u>

\sf \tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:

  • \theta = x
  • O = PV = 4 ft
  • A = RV = VQ = 15 ft

Substituting the given values into the formula and solving for x:

\implies \sf \tan(x)=\dfrac{4}{15}

\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)

\implies \sf x=14.9^{\circ}\:(nearest\:tenth)

As 14.9° is not between 18° and 27°, the roof is not safe.

-------------------------------------------------------------------------------------------------

<h3><u>Part (b)</u></h3>

<u>Pythagoras’ Theorem</u>

\sf a^2+b^2=c^2

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

  • a = RV = VQ = 15 ft
  • b = PV = 4 ft
  • c = PR

Substituting the given values into the formula and solving for PR:

\implies \sf 15^2+4^2=PR^2

\implies \sf 225+16=PR^2

\implies \sf PR^2=241

\implies \sf PR=\sqrt{241}

\implies \sf PR=15.5\:ft\:(nearest\:tenth)

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