A cactus casts a shadow 33 feet long. At the same time of day, Liam who is 6 feet tall, casts a shadow 9 feet long, as shown. 1) what’s the base of the larger triangle?

2)how tall is the cactus?

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here's the solution :-

1.) =》the base of the larger triangle is the length of shadow formed by cactus .

so, length of cactus is : 33 feet.

2.) now, jn the smaller triangle formed by liam and it's shadow : -

=》

since both triangle form 90° the bases of both the larger and smaller triangles are parallel , so the base angles of larger triangle = corresponding base angles of the smaller triangle

hence, the both triangles are similar

( by A.A postulate )

now since the both triangles are similar, the the sides will be proportional ,

=》

=》

=》

=》

so, length of the cactus = x = 22 feet

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