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Can anyone remember their days of studying GCSE trigonometry? My kid's trying to work out the surface area and angle of a rooftop.
House is 5m x 7m rectangle with a pitched roof from front to back. If you go into the loft, the middle of the roof is 220cm high.
So, you've basically got a right angled triangle with an opposite of 220cm and an adjacent of 350cm. Is it possible from this to work out the hypotenuse?
Then can you work out the surface area by multiplying the hypotenuse by 5m?
Then can you work out the angles by using Sin, Cos or Tan?
Cheers in advance.
House is 5m x 7m rectangle with a pitched roof from front to back. If you go into the loft, the middle of the roof is 220cm high.
So, you've basically got a right angled triangle with an opposite of 220cm and an adjacent of 350cm. Is it possible from this to work out the hypotenuse?
Then can you work out the surface area by multiplying the hypotenuse by 5m?
Then can you work out the angles by using Sin, Cos or Tan?
Cheers in advance.
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Only did CSE maths, and that 31 years ago.
The hypotenuse equals the square root of the sum of the squares of the other 2 sides. So hypothenuse = square root of (220^2 + 350^2) = 413.4 Yes you can work out the angles using sin etc. But can't remember how to do it now! All very simple stuff though. |
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a² + b² = c²
Where a and b represent the two sides you know and c = the diagonal. So if a = 3 ft and b = 3 ft, the two sides of your square a² = 3 x 3 and b² = 3 x 3 9 + 9 = c² 18 = c² √18 = 4.24 ft c = 4.24 ft being the square root of 18 |
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As far as the angle from memory you need to divide 220 by 350 then inverse tan the result. Though memory might be a but hazy.
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s = o / h
c = a / h t = o / a So TAN a = 220/350 =.62857 a= tan-1(.62857) = 32.15 degrees. Hyp^2 = 220^2 + 350 ^2 = 170900 hyp = sqrt(170900) =413.4cm However if it is only trig he is supposed to be doing then you can find the hypot out using sin or cos, after you have found the angle. |
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Thanks everyone.
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