Answer :
Answer:
[tex] h =\sqrt{390.731^2 -152.671^2}=359.670 ft [/tex]
Step-by-step explanation:
The situation is illustrated on the figure attached.
We can begin finding the values for h1 and h2 and in order to do this we can use the sine law.
[tex] \frac{sin (67)}{h_2} = \frac{sin (67)}{500}[/tex]
From this we have that [tex] h_2 = 500[/tex]
And for h1 we have this:
[tex] \frac{sin(67)}{500} = \frac{sin(46)}{h_1}[/tex]
And we got [tex] h_1 = \frac{sin(46)}{sin(67)} 500= 390.731 ft[/tex]
Now we cna use the Pythagorean identity, since we have two right triangles. If we apply this identity to the right triangle on the left we have this:
[tex] h^2 + x^2 = h^2_1[/tex] (1)
And for the right triangle we got:
[tex] h^2 +(500-x)^2 = h^2_2 [/tex] (2)
We can subctract equation (2) and (1) and we got:
[tex] (500-x)^2 -x^2 = h^2_2 -h^2_1[/tex]
And if we apply some algebra we got this:
[tex] 250000 -1000 x +x^2 -x^2 = 97329.185[/tex]
[tex] 250000 -1000 x = 97329.185[/tex]
[tex] 1000 x = 152670.815[/tex]
[tex] x =152.671[/tex]
Now since we have the value of x we can find the value for h like this:
[tex] h^2 = h^2_1 -x^2[/tex]
[tex] h =\sqrt{390.731^2 -152.671^2}=359.670 ft [/tex]
