Question

Find the value of x. Round to the nearest tenth.

Answer 1

1) x = 20. 8

2) x = 42.3

3) x = 13.0

4) x = 42.1

Explanation:

1) Use Sine

(Sine =
`(opposite)/(hypothenuse)`) Sine 53 =
`(x)/(26)`

(sine of 53 is 0.80) 0.80 =
`(x)/(26)`

(multiply 26 on both sides) 0.80 x 26 =
`(x)/(26)` x 26

(solve) 20.8 = x

2) Use Tan

(Tan =
`(opposite)/(adjacent)`) Tan 78 =
`(x)/(9)`

(tan of 78 is 4.70) 4.70 =
`(x)/(9)`

(multiply 9 on both sides) 4.70 x 9 =
`(x)/(9)` x 9

(solve) 42.3 = x

3) Use Cosine

(Cosine =
`\frac{adjacent} {hypothenuse}`) Cos 22 =
`(14)/(x)`

(cos of 22 is 0.93) 0.93 =
`(14)/(x)`

(multiply 14 on both sides) 0.93 x 14 =
`(14)/(x)` x 14

(solve) 13.02 = x

(round to the nearest tenth) 13.02 = 13.0

4) Use tan

(Tan =
`(opposite)/(adjacent)`) Tan 39 =
`(52)/(x)`

(tan of 39 is 0.809) 0.809 =
`(52)/(x)`

(multiply 52 on both sides) 0.809 x 52 =
`(52)/(x)` x 52

(solve) 42.068 = x

(round to the nearest tenth) 42.068 = 42.1