Question

Calculate the value of sin X to four decimal places

Answer 1

`\sin X = 0.7241`

Explanation:

For angle X, 2.0 ft is the adjacent leg. 2.9 ft is the hypotenuse.

The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

`\cos X = (adj)/(opp)`

`\cos X = (2.0)/(2.9)`

`\cos X = 0.689655`

Since we now know the value of cos X, we can find the value of sin X by using the trig identity

`\sin^2 X + \cos^2 X = 1`

`\sin^2 X + (0.689655)^2 = 1`

`\sin^2 X = 0.524376`

`\sin X = 0.7241`

Answer 2

0.7241

Explanation:

sin =
`(opposite)/(hypotenuse)`

In this case we have the hypotenuse (2.9) but not the opposite so here is how you calculate it

`a^(2)+b^(2)= c^(2) \\\\2^(2)+ b^(2)= 2.9^(2) \\4+ b^(2) = 8.41\\\\\sqrt{b^(2) }= √(4.41) \\b= 2.1`

So now you have the opposite (2.1)

so now you would divide
`(2.1)/(2.9) or 0.7241`