Question

How do I solve this?

Answer 1

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:

$x=rcos(\theta)$

Where x = 30m, $\theta=46$, and r is the hypotenuse which is to be determined and so:

$30=rcos(46)\\\\r=\frac{30}{cos(46)}$

Now we will input our r value into our y equation and so:

$y=rsin(\theta)\\\\y=(\frac{30}{cos(46)})sin(46)=30tan(46)=31.0659m$

So the height of the top triangle is 31.0659 meters.

Similarly let's calculate the height of the bottom triangle:

$x=rcos(\theta)\\\\30=rcos(62)\\r=\frac{30}{cos(62)}$

Now we'll plug it into our y equation:

$y=rsin(\theta)\\\\y=(\frac{30}{cos(62)})sin(62)=30tan(62)=56.4218m$

Therefore by adding the height of both triangles we obtain:

31.0659m + 56.4218m = 87.4877m