# trig

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a hedgehog wishes to cross a road without being run over. he observes the angle of elevation of a lamp post on the other side of the road to be 27 degrees from the edge of the road and 15 degrees from a point 10m back from the raod. How wide is the road??

• trig - ,

405 I THINK I *'S 15 BY 27 AND GOT 405. NOW THAT IVE HELPED YOU WITH TRIG CAN YOU HELP ME WITH INTRODUCTORY ALGEBRA

• trig - ,

2 rt. triangles are formed. The ver
side(y) is common to both triangles.

x = hor side of smaller triangle = Width of the RD.
(x + 10) = hor side of larger triangle

tan27 = y/x,
Eq1. y = x*tan27.

tan15 = y / (x + 10),
Eq2. y = (10 + x)tan15.

Substitute Eq1 for y in Eq2:
x*tan27 = (x + 10)*tan15,
x*tan27 = x*tan15 + 10*tan15,
x*tan27 - x*tan15 = 10*tan15,
0.5095x - 0.2679x = 2.679,
0.2416x = 2.679,

X = 2.679 / 0.2416 = 11.1 m. = Width of RD.

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