# A Carpenter Makes Stools for Electricians with a Square Top of Side 0.5 M and at a Height of 1.5 M Above the Ground. Also, Each Leg is Inclined at an Angle of 60° to the Ground. Find the Length of Each Leg and Also the Lengths of Two Steps to Be Put at Equal Distances. - Mathematics

A carpenter makes stools for electricians with a square top of side 0.5 m and at a height of 1.5 m above the ground. Also, each leg is inclined at an angle of 60° to the ground. Find the length of each leg and also the lengths of two steps to be put at equal distances.

#### Solution

Let the length of stool,AB = 0.5 m, height AC = 1.5 m and its leg inclined at an angle of 60° to the ground.

Let the length of leg AE = hm

We have to find the length of leg, lengths of two steps equal in length.

in ΔAEC, ∠AEC = 60°

sin 60° = (AC)/(AE)

=> sqrt3/2 = 1.5/h

=> h = 3/sqrt3

=> h = 1.732

In  ΔAGH, ∠AGH = 60° and AH = 0.5 m

tan 60^@ = (AH)/(GH)

=> sqrt3 = 0.5/GH

=> GH = 0.5/sqrt3

=> GH = 0.2886

Total length  = 0.5 + (0.2886 xx 2) = 1.1077 m

In Δ APQ, ∠APQ =  60° and AQ = 1 m

tan 60^@ = (AQ)/(PQ)

=> sqrt3 = 1/Pq

=> PQ = 1/sqrt3

=> PQ = 0.577

Total lengths 0.5 + (0.577 x 2) = 1.654 m

Hence  the length of leg is 1.732 m

And length of eacb are 1.1077 m and 1.654 m

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.1 | Q 57 | Page 33