anonymous
  • anonymous
Martin is painting his house and needs to reach a point 9 feet above the ground. He places a 10.5-foot-long ladder against the house so that it forms an angle of (theta) with the ground. Describe the triangle that is formed by the ground, the house, and the ladder. Identify the hypotenuse, the adjacent side, and the opposite side. To the nearest tenth of a degree, find the angle the ladder forms with the ground.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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e.mccormick
  • e.mccormick
Did you try a simple sketch and labling these?
e.mccormick
  • e.mccormick
|dw:1370986895525:dw|
e.mccormick
  • e.mccormick
Ad some numbers, use Pythagoras as your friendly theorem of the day, and be done!

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More answers

jdoe0001
  • jdoe0001
|dw:1370987193591:dw|
e.mccormick
  • e.mccormick
Well, and use the trig ratios to get the right angle.
e.mccormick
  • e.mccormick
correct angle.... since the right angle has a special meaning here.
anonymous
  • anonymous
Ladder = c, house = a a^2 + b^2 = c^2 a^2 = 81 c^2 = 110.25 110.25 - 81 = 29.25 sqrt of 29.25 = 5.4
jdoe0001
  • jdoe0001
|dw:1370987285806:dw|
anonymous
  • anonymous
right?
e.mccormick
  • e.mccormick
Well, they wanted the sides identified, which may include the 5.4, but you also need to get the angle \(\theta\).
e.mccormick
  • e.mccormick
And what trig ratio is \(\cfrac{Opp}{Hyp}\)
anonymous
  • anonymous
sin. so opposite (9) divided by hypotenuse (10.5) is .86
e.mccormick
  • e.mccormick
And take the arcsin of that to get theta.
anonymous
  • anonymous
sin^-1(.86) = 59.3
e.mccormick
  • e.mccormick
Yep. That way you can mark all the sides, and the angle, which should easily be all the things they ask for.
anonymous
  • anonymous
How would I find the angle of the adjacent?
e.mccormick
  • e.mccormick
And you have a bit of a rounding error there... Might want to just put the improper fraction into your calculator.
e.mccormick
  • e.mccormick
Once you have one angle, you can use the law of sines to solve the side.... but that can be less acculturate at times...
e.mccormick
  • e.mccormick
|dw:1370987704496:dw|
anonymous
  • anonymous
hahahahaha. so to find the length of the ground between the ladder and the house, what would i do?
e.mccormick
  • e.mccormick
What you did. \(10.5^2-9^2=a^2\)
e.mccormick
  • e.mccormick
And that would be the adjacent side....
anonymous
  • anonymous
I need help with one more similar question, but I only need to know how to draw out my triangle so I can find the values. Here's what it says: In triangle ABC, C is a right angle. Side c = 9 and side a = 5. What are the measures of the remaining sides and angles, in degrees, of the triangle? So C can't be the hypotenuse. How would I draw it?
e.mccormick
  • e.mccormick
BTW: With putting in the actual fraction, I got 59.0 as the nearest 10th of a degree.
anonymous
  • anonymous
|dw:1370988142944:dw|
e.mccormick
  • e.mccormick
No, c MUST be the Hypotenuse because C is the right angle.
anonymous
  • anonymous
How does the hypotenuse form a right angle?
anonymous
  • anonymous
The hypotenuse is always the side that closes off the L shape (in this example anyway), right? The opposite is always the side opposite of the angle.
e.mccormick
  • e.mccormick
|dw:1370988241547:dw| The hypotenuse of a right traingle is always opposite the right angle because it is ALWAYS the largest angle. In a right triangle the angls are A+B+90=180, therefore A+B=90. For that to be true, both A and B must be < 90!
e.mccormick
  • e.mccormick
Oops. c=9... Hit wronmg key there.
anonymous
  • anonymous
So C is the hypotenuse, but in terms of angles, C is the right angle?
e.mccormick
  • e.mccormick
Also, A, B, C are angles. a, b, c are sides.
anonymous
  • anonymous
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOH gotcha.
e.mccormick
  • e.mccormick
Yes, C=90 and c=9.
anonymous
  • anonymous
I can't believe I never heard or understood that. My mistake. Thank you so much, you've been a great great help.
e.mccormick
  • e.mccormick
np. have fun! Sometimes it is the simple things a teacher or book skips that mess us up.
anonymous
  • anonymous
@jdoe0001

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