Question

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

Answer 1

From the law of sines, we have

`l = h\sin(\theta) = h\cos(\alpha)`

where
`l` is the leg we're interested in,
`h` is the hypothenuse,
`\theta` is the angle opposite to
`l`, and
`\alpha` is the angle between
`l` and
`h`.

So, in the first case, we can use

`x = 15\sin(35) \approx 8.6`

And in the second excercise, we use

`x = 11\cos(44) \approx 7.6`

Answer 2

x=8.6 m, and x=7.9 ft

Explanation:

Hello, I think I can help you with this

this is a right triangle, which means we can use a trigonometric relationship that relates the angle, the hypotenuse and the opposite side

Let's remember

`sin(\alpha )=(opposite\ side)/(hypotenuse) \\and\\cos(\alpha)=(adjacent\ side)/(hypotenuse) \\`

Step 1

P.41

Let

α=35 degrees

hypotenuse= 15m

opposite side =unknown= x

replacing

`sin(\alpha )=(opposite\ side)/(hypotenuse) \\sin(35)=(x)/(15\ m)\\ to\ isolate\ x, multiply\ each\ side by\ 15 m\\15 m*sin(35)=x\\x=15\ m*(0.57)\\x=8.6\ m\\`

Step 2

(second triangle p.42)

Let

α=44 degrees

hypotenuse= 11 ft

adjacent side =unknown= x

replacing

`cos(\alpha )=(adjacent\ side)/(hypotenuse) \\cos(44)=(x)/(11\ ft)\\ to\ isolate\ x, multiply\ each\ side by\ 11 ft\\11 ft*cos(44)=x\\x=11\ ft*(0.71)\\x=7.9\ ft\\`

I hope it helps, have a nice day