Question

please solve this problem​

Answer 1

Given :

• AB perpendicular to BC
• angle(ACB) = 30°
• BC = √(300) m

To find :

Length of AB

Solution :

As we can see closed figure ABC is a. triangle!

Also we are given that AB is perpendicular to BC, this gives that angle(ABC) = 90°. Therefore ∆ABC is a right angle triangle.

Now we can use trigonometric ratio.

We know that ,

$\sf \tan( \theta) \: = \: \dfrac{perpendicular}{base}$

$\sf \implies \: \tan(30 {}^{\circ}) = \dfrac{AB}{BC}$

$\sf \implies \: \tan(30 {}^{\circ}) = \dfrac{AB}{ \sqrt{300} \: m}$

$\sf \implies \: \dfrac{1}{ \sqrt{3} } \: = \: \dfrac{AB}{ \sqrt{300} \: m}$

$\sf \implies \: \: {AB} \: = \sqrt{300} \: \times \dfrac{1}{ \sqrt{3} } \:m$

$\sf \implies \: \: {AB} \: = \sqrt{\dfrac{300}{ 3 }} \: \:m$

$\sf \implies \: \: {AB} \: = \sqrt{100} \: \:m$

$\sf \implies \: \: {AB} \: = \pm \: 10 \: \:m$

Note - AB is a side and hence cannot be negetive

$\sf \implies \: \: {AB} \: = \bold{10\: \:m}$

ANSWER :

Option A) 10m

Answer 2

$\sf{Given}$

•AB perpendicular to BC

•angle(ACB) = 30°

•BC = √(300) m

$\sf{To ~find :}$

•Length of AB

$\sf{Solution :}$

•As we can see closed figure ABC is a triangle!

So As We know that ,

$\rm\tan( \theta) \: = \: \dfrac{perpendicular}{base}$

$\rm\implies \: \tan(30 {}^{\circ}) = \dfrac{AB}{BC}$

$\rm\implies \: \tan(30 {}^{\circ}) = \dfrac{AB}{ \sqrt{300} \: m}$

$\rm\implies \: \dfrac{1}{ \sqrt{3} } \: = \: \dfrac{AB}{ \sqrt{300} \: m}$

$\rm \implies \: \: {AB} \: = \sqrt{300} \: \times \dfrac{1}{ \sqrt{3} }$

$\sf \implies \: \: {AB} \: = \sqrt{\dfrac{300}{ 3 }} \\ \\ \sf \implies \: \: {AB} \: = \sqrt{100} \\ \\ \sf \implies \: \: {AB} \: = \pm \: 10 \: \:m$

$\implies \: \: {AB} \: = \bold{10\: \:m}$

ANSWER :

⊙ 10m is the answer!!