A vertical lamppost of height 6 m is at P When Sam stands at the point A. the shadow formed is 2.1 m long. When Sam stands at th

Question

2 years ago

10

e point B, 13.3 m away from A, the shadow formed is 3.6 m long
(1) How tall is Sam?

(i) Find angle A'OB

1 answer:

Damm [24] · Answer 1 · 2023-06-27T08:08:31+03:00

Step-by-step explanation:

triangle ADA' and OPA' are similar so, using property of similar triangles :

6/AD = (13.3+3.6-PB'+2.1)/2.1

{A'P = 13.3 +3.6 - PB' + 2.1}

6/AD = (16.9-PB'+2.1)/2.1

6/AD = (19-PB')/2.1 - EQN I

As we know, AD = BC as both of them are Sam's height (constant)

triangle OPB' and BCB' are similar so, using property of similar triangles:

6/BC = PB'/3.6

OR, 6/AD = PB'/3.6 (AD = BC) - EQN II

Now,

comparing EQN I AND II we get :

(19-PB')/2.1 = PB'/3.6

or, 68.4 - 3.6PB' = 2.1PB'

or, 68.4 = 5.7PB'

so, PB' = 12 m

Now, as we know,

6/BC = PB'/3.6

OR, 6/BC = 12/3.6

OR, (6×3.6)/12 = BC

So, the height of Sam is 1.8 m.

tanA' = AD/AA'

<A' = tan‐¹(1.8/2.1)

<B' = tan‐¹(1.8/3.6)

Now,

<A'OB' = 180 - tan‐¹(1.8/2.1) - tan‐¹(1.8/3.6)

<A'OB' = 112.833