Question

I don't get this trigonometry question

Answer 1

`\sin X=(3)/(5)`

Explanation:

Sine trigonometric ratio

`\sf \sin(\theta)=(O)/(H)`

where:

• θ is the angle.
• O is the side opposite the angle.
• H is the hypotenuse (the side opposite the right angle).

From inspection of the given diagram:

• The side opposite angle X is 24 units.
• The hypotenuse (longest side of the right triangle) is 40 units.

Therefore:

• θ = X
• O = 24
• H = 40

Substitute the values into the sine trigonometric ratio:

`\implies \sin X=(24)/(40)`

We can reduce the fraction to its smallest equivalent by dividing the numerator and denominator by 8:

`\implies \sin X=(24 / 8)/(40 / 8)=(3)/(5)`

Answer 2

• 3/5 or 0.6

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Definition of sine:

• Sine of angle = opposite leg / hypotenuse

The angle is X, opposite leg is YZ = 24, hypotenuse is XZ = 40.

Substitute the values and find the sine of angle X:

• sin X = 24 / 40 = 3/5 or 0.6