What Will be the height (AO) of the triangle if $∠$ ABO given is changed from $45^{\circ}$ to $60^{\circ}$ ?

$\sqrt{3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$2 \sqrt{3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\sqrt{6}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$3 \sqrt{3}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
$\sqrt{6}$

When $∠$ ABO is changed to $60^{\circ}$ , we get the above figure.

$∴$ $△$ AOB is a 30-60-90 triangle.

$\Rightarrow$ the sides are in the ratio 1 : $\sqrt{3}$ : 2

Let BO = x , AO = $\sqrt{3}$ x and AB = 2x

Given: AB = $2 \sqrt{2}$

$\Rightarrow$ $2 \sqrt{2}$ = 2x

$\Rightarrow$ x = $\sqrt{2}$

$∴$ AO = $\sqrt{3}$ x = $\sqrt{3} \times \sqrt{2}$ = $\sqrt{6}$

Suggest Corrections

Similar questions

The angle of elevation of the top of a tree from a point A on the ground is $60^{\circ}$ .On walking 20 m away from its base, to a point B, the angle of elevation changes to $30^{\circ}$ . Find the height of the tree.

If f (x) = | cos x - sin x |

, then

f^{'} (\frac{π}{6})

is equal to

Q. The area of triangle formed by the tangent, normal drawn at

(1, \sqrt{3})

to the circle

x^{2} + y^{2} = 4

and positive x-axis, is

If b is the mean proportion between 3 and 9 , b value is :

Q. If the ratio of the mole fraction of a solute is changed from

\frac{1}{3}

\frac{1}{2}

in the 800 g of solvent then the ratio of molality will be :

Join BYJU'S Learning Program

What Will be the height (AO) of the triangle if ∠ ABO given is changed from 45∘ to 60∘?

The correct option is C √6 When ∠ ABO is changed to 60∘, we get the above figure. ∴ △ AOB is a 30-60-90 triangle. ⇒ the sides are in the ratio 1 : √3 : 2 Let BO = x , AO = √3x and AB = 2x Given: AB = 2√2 ⇒ 2√2 = 2x ⇒ x = √2 ∴ AO = √3 x = √3×√2 = √6

What Will be the height (AO) of the triangle if $∠$ ABO given is changed from $45^{\circ}$ to $60^{\circ}$ ?