Current location - Health Road Network - Medical equipment - (2014?Lianyungang) In a science and technology activity, Xiaoming conducted a simulated radar scanning experiment. As shown, the dial is △ABC, where AB = AC, ∠BAC = 1

(2014?Lianyungang) In a science and technology activity, Xiaoming conducted a simulated radar scanning experiment. As shown, the dial is △ABC, where AB = AC, ∠BAC = 1

Solution: (1) As shown in Figure 1, make AD ⊥ BC at point A, and the foot of the pendant is D.

∵∠BAC=120°, AB=AC,

∴∠ABC=∠C=30°.

Let AB=2tcm.

In Rt△ABD, AD=

1
2
AB=t, BD=
3
2
AB=
3
t.

In Rt△AMD, ∵∠AMD=∠ABC+∠BAM=45°,

∴MD=AD=t.

∵ BM=BD-MD. i.e.

3
t-t=20
3
-20.

Solve for t = 20.

∴AB=2×20=40cm.

Answer: the length of AB is 40cm.

(2) As shown in Figure 2, when the light is rotated for 6 seconds,

Set AP to intersect BC at the point N. At this time, the ∠BAN=15°×6=90°.

In Rt△ABN, BN=

AB
cos30°
=
40
3
2
=< td style="border-bottom:1px solid black;padding-bottom:1px;font-size:90%">80
3
3
.

∴The ray AP is rotated for 6 seconds, and the intersection N with BC is at a distance from point B

80
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