Question

Δ XYZ is right angled at Y. If m∠Z = 60°, what is the length of YZ (in cm), if ZX = 3√3 cm?

A) 3√3/2 B) 3√3 C) 9 D) 6

Answer 1

D - 6

Step-by-step explanation:

<z =60°

right angle at Y =90° because right angle is = 90°

so, 90° + 60° = x°

= x°= 90+60°

x° = 150°

150° = 150°/90° = 60° = 6

6 ans.

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Answer 2

The length of YZ (in cm) is (A) 3√3 / 2 cm.

Given: Δ XYZ is right angled at Y and ∠Z = 60°, ZX = 3√3 cm.

To Find: The length of YZ (in cm).

Solution:

• We shall make use of some trigonometrical identities to solve this numerical.

• We know that in a right-angled triangle, there is a base, a perpendicular, and a hypotenuse concerning the angle which is equal to 90°.

• Accordingly, we can say that;

          tan A = Perpendicular / Base                                          ...(1)

           sin A = Perpendicular / Hypotenuse                             ...(2)

          cos A = Base / Hypotenuse                                            ...(3)

Also, the Pythagoras theorem states that;

          ( Hypotenuse )² = ( Perpendicular )² + ( Base )²             ...(4)

Coming to the numerical, we r given;

Δ XYZ is right angled at Y.

 ∠ Z = 60°, ZX = 3√3 cm.

We can visualize that ZX is the Hypotenuse of the Δ XYZ.

Let us consider the lengths of XY and YZ to be 'x' and 'y' respectively.

Accordingly from (1), we can say that;

           tan Z = Perpendicular / Base  = XY / YZ

       ⇒ tan 60° = x / y

       ⇒ x = y√3                                                                        ...(5)

From (2), we can say that;

           sin Z = Perpendicular / Hypotenuse

       ⇒ sin 60° = XY / 3√3

       ⇒ √3 / 2 = x / 3√3

       ⇒  x = 9 / 2

From (3), we can say that;

           cos Z = Base / Hypotenuse          

        ⇒ cos 60° = YZ / 3√3

        ⇒ 1/2 = y / 3√3

        ⇒ y = 3√3 / 2

So, YZ = 3√3 / 2 cm.

Hence, the length of YZ (in cm) is (A) 3√3 / 2 cm.

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