Answer:
87.4877 meters
Step-by-step explanation:
First we can make two right triangles as shown on the images below. So first let's calculate the height of the top triangle:
[tex]x=rcos(\theta)[/tex]
Where x = 30m, [tex]\theta=46[/tex], and r is the hypotenuse which is to be determined and so:
[tex]30=rcos(46)\\\\r=\frac{30}{cos(46)}[/tex]
Now we will input our r value into our y equation and so:
[tex]y=rsin(\theta)\\\\y=(\frac{30}{cos(46)})sin(46)=30tan(46)=31.0659m[/tex]
So the height of the top triangle is 31.0659 meters.
Similarly let's calculate the height of the bottom triangle:
[tex]x=rcos(\theta)\\\\30=rcos(62)\\r=\frac{30}{cos(62)}[/tex]
Now we'll plug it into our y equation:
[tex]y=rsin(\theta)\\\\y=(\frac{30}{cos(62)})sin(62)=30tan(62)=56.4218m[/tex]
Therefore by adding the height of both triangles we obtain:
31.0659m + 56.4218m = 87.4877m
