A ladder leans against a wall . Its foot is 3m away from the wall and making an angle 35 degree with ground. How high is the other end of the ladder from the ground? (sin 35°= 0.57. cos 35°=0.82, tan 35º = 0.70)
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Since sin 30 deg = 0.5, the length of wall between the ladder and the ground is half the length of the ladder (the hypotenuse of this right triangle). Using one of the trig identities (sin^2 + cos^2 = 1), we can substitute 30 deg for the angle and write:
sin^2 (30 deg) + cos^2 (30 deg) = 1 or
(1/2)^2 + cos^2 (30 deg) = 1 or cos^2 (30 deg) = 1 - 1/4 = 3/4. Therefore,
cos (30 deg) = (sq rt 3)/2
We know that the cos of an angle is equal to the ratio of the side adjacent to the angle with the hypotenuse (h). We are given that the adjacent side is 3 m in length. So
cos (30 deg) = 3/h = (sq rt 3)/2, or h = 3*2/(sq rt 3) = 2(sq rt 3) = 3.46 m, the length of the ladder.
@chillwildlife:)
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