Question

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

Answer 1

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

$sin(\alpha )=\frac{opposite\ side}{hypotenuse} \\and\\cos(\alpha)=\frac{adjacent\ side}{hypotenuse}$

Step 1

P.41

Let

α=35 degrees

hypotenuse= 15m

opposite side =unknown= x

replacing

$sin(\alpha )=\frac{opposite\ side}{hypotenuse} \\sin(35)=\frac{x}{15\ m}\\ to\ isolate\ x, multiply\ each\ side by\ 15 m\\15 m*sin(35)=x\\x=15\ m*(0.57)\\x=8.6\ m$

Step 2

(second triangle p.42)

Let

α=44 degrees

hypotenuse= 11 ft

adjacent side =unknown= x

replacing

$cos(\alpha )=\frac{adjacent\ side}{hypotenuse} \\cos(44)=\frac{x}{11\ ft}\\ to\ isolate\ x, multiply\ each\ side by\ 11 ft\\11 ft*cos(44)=x\\x=11\ ft*(0.71)\\x=7.9\ ft$

I hope it helps, have a nice day

Answer 2

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

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