Answer:
a) not safe
b) 15.5 ft (nearest tenth)
Step-by-step explanation:
Part (a)
Tan trig ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
Given:
- [tex]\theta[/tex] = x
- O = PV = 4 ft
- A = RV = VQ = 15 ft
Substituting the given values into the formula and solving for x:
[tex]\implies \sf \tan(x)=\dfrac{4}{15}[/tex]
[tex]\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)[/tex]
[tex]\implies \sf x=14.9^{\circ}\:(nearest\:tenth)[/tex]
As 14.9° is not between 18° and 27°, the roof is not safe.
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Part (b)
Pythagoras’ Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(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:
[tex]\implies \sf 15^2+4^2=PR^2[/tex]
[tex]\implies \sf 225+16=PR^2[/tex]
[tex]\implies \sf PR^2=241[/tex]
[tex]\implies \sf PR=\sqrt{241}[/tex]
[tex]\implies \sf PR=15.5\:ft\:(nearest\:tenth)[/tex]
