Question

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.

Answer 1

length of each leg = √3m=1.732m

lengths of two steps to be put at

1/√3m and 2/√3m

• In triangle ABC

• Sin60°= P/H=AB/AC=√3/2

• AB/AC=√3/2

•1.5/AC=√3/2

• AC = √3m

• Now , for steps two points will be

at 0.5m , 1.0m from ground

• Using sine we get the two points

as 1/√3m &2/√3m on the leg

Answer 2

The length of each leg is 1.732 m

The length of two steps are 1.1077 m and 1.654 m

Explanation:

Given that the carpenter makes stools 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.

We need to find the length of each leg and the length of two steps.

Let ABEF be the stool with a height AC with legs AE and BF.

Thus, we have, $A B=0.5 \ {m}$ and $\mathrm{AC}=1.5 \mathrm{m}$

$\angle A E C=60^{\circ}$

Let us consider the triangle AEC.

$\sin 60^{\circ}=\frac{A C}{A E}$

     $\frac{\sqrt{3}}{2}=\frac{1.5}{h}$

       $h=\frac{3}{\sqrt{3}}$

       $h=1.732 \ m$

Now, let us consider the triangle AGH.

$\tan 60^{\circ}=\frac{A H}{G H}$

Since, from the figure, we can see that , $\angle \mathrm{AGH}=60^{\circ}$ and $A H=0.5 \mathrm{m}$

Substituting the values, we have,

 $\sqrt{3}=\frac{0.5}{GH}$

$G H=\frac{0.5}{\sqrt{3}}$

$G H=0.2886 \ m$

Thus, the total length of the step 1 is $\mathrm{GH}+\mathrm{HT}+\mathrm{TU}=0.5+(0.2886 \times 2)=1.1077 \mathrm{m}$

Let us consider the triangle APQ

$\tan 60^{\circ}=\frac{A Q}{P Q}$

Since, we know that $\angle \mathrm{APQ}=60^{\circ}$ and $A Q=1 \ {m}$

Substituting the values, we have,

$\sqrt{3}=\frac{1}{PQ}$

$P Q=\frac{1}{\sqrt{3}}$

$P Q=0.577 \ m$

Thus, the total length of the step 2 is $\mathrm{PQ}+\mathrm{QR}+\mathrm{RS}=0.5+(0.577 \times 2)=1.654 \mathrm{m}$

Therefore, the length of the leg is 1.732 m and the length of two steps are 1.1077 m and 1.654 m

Learn more:

(1) A carpenter makes stool for electrician with 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 length of two steps to be put at equal distances

brainly.in/question/1234866

(2) 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

brainly.in/question/5701898