HELP ASAP GEOMETRY 40 POINTS Use the image to answer the following questions.

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

Part (a)

It's not stated, but I'm assuming that RV = VQ

If so, then we use the tangent ratio to connect the opposite side PV = 7 and adjacent side RV = 16

Focus on triangle RPV

tan(angle) = opposite/adjacent

tan(R) = PV/RV

tan(x) = 7/16

x = arctan(7/16) same as inverse tangent

x = 23.6293777 which is approximate

Rounding to the nearest degree, the angle x is roughly 24 degrees.

Since 18 < 24 < 27, this means the roof pitch follows the safety guidelines.

Part (b)

Again we only focus on triangle RPV

We have two pathways we can take. The first option is to use the pythagorean theorem

a^2+b^2 = c^2

c = sqrt(a^2 + b^2)

PR = sqrt( (RV)^2 + (PV)^2 )

PR = sqrt( (16)^2 + (7)^2 )

PR = 17.464249 approximate

PR = 17.5

The second path you could take is to use the angle x we found in part (a). Use either the cosine or sine ratios like so

sin(angle) = opposite/hypotenuse

sin(x) = PV/PR

PR = PV/sin(x)

PR = 7/sin(23.6293777)

PR = 17.464249

PR = 17.5

The pathway for cosine will look almost identical to this, but you'll be computing PR = RV/cos(x) instead.

x+20⩾50

Step-by-step explanation:

in inequality, the word at least means that is equal or more than. so that means that Allie might equal or more than 50 hours in the model but if you're to solve it, Allie will need 30 or more hours. and since she already has 20, add the 20.