Question

A carpenter make s a stool for electric Ian's with the square top of side 0.5m and at a height of 1.5m above the ground. Also each leg is inclined at an angle of 60degree to the ground. Find the length of each leg and also the length of 2 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 ≅ ΔDBJS

RJ = JS

RS = RJ + JJ + JS

= 0.28 + 0.5 + 0.28

= 1.06 m

(iii) In ΔAKL,

tan 60° =



LK = m

Similarly, ΔAKL ≅ ΔBKM

LK = KM

Length of step LM = LK + KK + KM

= + 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

Answer 2

Before solving this question, it is required for you to have at least basic knowledge of trigonometric ratios and similarity of triangles.

I suggest you to read the whole solution as shown in the image and try to understand it step by step, and question at any point that you find difficult.

Also, I have taken the value of √3 as exactly 1.73, so the answer might vary from the original to 2 decimal places.

Hope this helps.

(And if there's any calculation mistake then please notify me, so I shall provide the correct answer)