SOLUTION: A triangle is formed by the x-axis and the lines 5y=9x and 5x+9y=45. a) Find the angles of inclination of the two lines. (nearest degree) b) What sort of triangle has been formed

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Question 1191786: A triangle is formed by the x-axis and the lines 5y=9x and 5x+9y=45.
a) Find the angles of inclination of the two lines. (nearest degree)
b) What sort of triangle has been formed?
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
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A triangle is formed by the x-axis and the lines 5y=9x and 5x+9y=45.
a) Find the angles of inclination of the two lines. (nearest degree)
b) What sort of triangle has been formed?
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From equation 5y = 9x you have  y = %289%2F5%29x.

    So the slope of this straigh line is  m%5B1%5D = 9%2F5

    and the angle "a" with x-axis is  tan(a) = m%5B1%5D = 9%2F5,  a = arctan%289%2F5%29 = 60.9454 degrees (rounded).



From equation 5x + 9y = 45 you have  y = %28-5%2F9%29x+%2B+5.

    So the slope of this straigh line is  m%5B2%5D = -5%2F9

    and the angle "b" with x-axis is  tan(b) = m%5B2%5D = -5%2F9,  a = arctan%28-5%2F9%29 = -29.0546 degrees (rounded).



Since the slopes  m%5B1%5D  and  m%5B2%5D  are  negative reciprocal  ( m%5B1%5D.m%5B2%5D = -1 ),

the lines are perpendicular and the triangle is a right angled triangle.

Solved.