Question

a carpenter makes stools for electricians of side 0.5 m and at a height of 1.5m above the ground .also each leg is inclined at an angle of 60 degree to the ground. Find the lenght of each leg and also the lenghts of two steps to be put at equal distances

Answer 1

Let AC & BD be the length and AB be the edge of the top of the top of the stool.

AP = 1.5 m

AJ = JK = KP = 

(i) ΔAPC

∠P = 90°

sin C = 

⇒ sin60° = 

⇒ 

⇒ AC = 

⇒ AC = 1.732 m

In ΔAPC & ΔBQD

∠C = ∠D, ∠P = ∠Q, AP = BQ

ΔAPC ≅ ΔBQD  [By RHS congruence criterion]

In ΔAJR

Tan 60° = 

⇒ RJ 

⇒ RJ = 0.28 m.

(ii) ΔAJR ≅ ΔDBJ’S

RJ = J’S

RS = RJ + JJ’ + J’S

= 0.28 + 0.5 + 0.28

= 1.06 m

(iii) In ΔAKL,

tan 60° = 

LK =  m

Similarly, ΔAKL ≅ ΔBK’M

LK = K’M

Length of step LM = LK + KK’ + K’M

                        =  + 0.5 + 

                        = 3.96 m

Leg AC = leg BD = 1.732 m

Length of step RS = 1.06 m

Length of step LM = 3.96 m