Respuesta :

From the law of sines, we have

[tex] l = h\sin(\theta) = h\cos(\alpha)[/tex]

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

So, in the first case, we can use

[tex] x = 15\sin(35) \approx 8.6 [/tex]

And in the second excercise, we use

[tex] x = 11\cos(44) \approx 7.6 [/tex]

Answer:

x=8.6 m, and x=7.9 ft

Step-by-step 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

[tex]sin(\alpha )=\frac{opposite\ side}{hypotenuse} \\and\\cos(\alpha)=\frac{adjacent\ side}{hypotenuse} \\[/tex]

Step 1

P.41

Let

α=35 degrees

hypotenuse= 15m

opposite side =unknown= x

replacing

[tex]sin(\alpha )=\frac{opposite\ side}{hypotenuse} \\sin(35)=\frac{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\\[/tex]

Step 2

(second triangle p.42)

Let

α=44 degrees

hypotenuse= 11 ft

adjacent side =unknown= x

replacing

[tex]cos(\alpha )=\frac{adjacent\ side}{hypotenuse} \\cos(44)=\frac{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\\[/tex]

I hope it helps, have a nice day

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