F.3 Math Trigo/gradient

a)the distance of PQ
= (1.6)(80)
= 128m
the vertical distance between P and Q = 300﹣200 = 100m
tanθ= 100 / 128
θ= 0.78125
θ= 38.0度
∴ the inclinations of PQ = 38.0度
QR = (3.2)(80) = 256m
the vertical distance between P and Q = 500﹣300 = 200m

tanθ= 200 / 256
θ= 0.78125
θ= 38.0度
∴ the inclinations of QR = 38.0度
Since tanθof PQ = tanθof QR
∴PQ and QR have the same gradients.

b)the distance of PR
= (128 + 256)m
= 384m
the vertical distance between P and Q = 500﹣200 = 300m
∴tanθ= 300/384
tanθ= 0.78
the gradient of PR = 0.78

c)By using the Pythagorean theorem,
(the actual length of PR)^2 = 300^2 + 384^2
(the actual length of PR)^2 = 237456
the actual length of PR = √ 237456
the actual length of PR = 487m


2008-04-23 19:39:04 補充：
你可以用圖片來理解：
http://s248.photobucket.com/albums/gg191/ncy_0916/?action=view&current=f3maths2-1.jpg