Question

I calculated 3:4 but the answer scheme said that it should be 4:3, please explain why, thanks !

Answer 1

C. 4 : 3

Explanation:

From the diagram attached below, we can see the ratios of the sides of the triangle.

The question asks us to find the ratio of sin ∠X : sin ∠Z. To solve this, we have to know the definition of sine of an angle Θ:

`\boxed{\mathrm{sin \theta = (opposite)/(hypotenuse)}}`.

For • ∠X: opposite side ⇒ YZ = 4

hypotenuse ⇒ XZ = 5

• ∠Z: opposite side ⇒ XY = 3

hypotenuse ⇒ XZ = 5

Therefore,

sin ∠X : sin ∠Z

=
`(4)/(5)` :
`(3)/(5)`

= 4 : 3 [Multiplying both sides by 5]

Therefore, the ratio sin ∠X : sin ∠Z = 4:3.