anonymous
  • anonymous
Refer to the following diagram for the roof of a house. In the figure, x is the length of a rafter measured from the top of a wall to the top of the roof; θ is the acute angle between a rafter and the horizontal; and h is the vertical distance from the top of the wall to the top of the roof. Suppose that θ = 32° and h = 37.5 ft. (a) Determine x. Round the answer to one decimal place. (b) Find the area of the gable. Round the final answer to one decimal place. [The gable is the triangular region bounded by the rafters and the attic floor.]
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
anyooooooooooooone?
anonymous
  • anonymous
Since we are given a right triangle we know that \[\sin(x)=\frac{opp}{hyp}=\frac{37.5}{hyp}=\sin(32)\] Our hypotenuse being $x$ in this case. From here we find the area of the triangle with \[A=\frac{1}{2}base \times height\] so we need to find the base. How do we do this? Well \[\cos(x)=\frac{adj}{hyp}\] and since we discovered the hypotenuse in the previous part of the problem this should be fairly simple. Hope this helps!

Looking for something else?

Not the answer you are looking for? Search for more explanations.