Question

Trigonometry help finding the value of x

Answer 1

`5√(3)` or 8.66

Explanation:

use tan:

tan =
`(opposite)/(adjacent)`

⇒ tan 60 =
`(x)/(5)`

tan of 60 is 1.73

⇒ 1.732 =
`(x)/(5)`

multiply 5 on both sides

⇒ 1.732 x 5 =
`(x)/(5)` x 5

⇒ 8.66

Answer 2

`\boxed {\boxed {\sf D. \ 5 \sqrt 3 \ or \ 8.66}}`

Explanation:

Remember the 3 main trigonometric ratios:

• sinθ= opposite/hypotenuse
• cosθ= adjacent/hypotenuse
• tanθ= opposite/adjacent

We are given the 60 degree angle. 5 is adjacent to the angle and x is opposite. Therefore, we must tangent.

`tan \theta= \frac {opposite}{adjacent}`

`tan60=\frac {x}{5}`

Since we are solving for x, we must isolate that variable. It is being divided by 5 and the inverse of division is multiplication. Multiply both sides by 5.

`5(tan60)=\frac {x}{5} *5`

`5(tan60)=x\\5*$$1.73205080757= x\\8.66025403784=x`

If we round to the nearest hundredth, the 0 in the thousandth place tells us to leave the 6.

`8.66 \approx x`

x is about 8.66 or 5√3, which is choice D.