Question

Find the lengths of RS and QS

Answer 1

RS = 7√3 and QS = 14

Explanation:

If angles of right angled triangle are 30, 60 and 90 then the sides are in the ratio, 1:√3 : 2

From the given figure we get,

Triangle QRS is a right angled triangle, right angled at R.

And also <R = 90° and <S = 30°

Then <Q = 60°

To find RS and QS

The sides of triangle QRS are 30,60 and 90

The sides of sides are,

QR : RS : QS = 1:√3 : 2

QR = 7 then RS = 7√3 and QS = 14

Answer 2

Option C. RS= 7√3 ,QS = 14

Explanation:

In the given question a right angle triangle has been given with an angle ∠QSR=30° and one side QR=7.

As we know from trigonometry rules in any triangle ΔQRS

Sin∅ = Height/ Hypotenuse

From this formula we can get the length of QS

Sin 30° = 7/ QS

Since Sin 30°= 1/2

Then 1/2 = 7/QS

⇒ QS = 7×2 =14

Now to get the length of base RS we will use the fact

Cos ∅ = Base/Hypotenuse

Cos 30°= RS/Hypotenuse(QS)

Since Cos 30°=(√3)/2

Therefore (√3)/2 = RS/14

RS = 14(√3)/2 = 7√3

So the lines RS= 7√3 and QS = 14