Question

Two people located 500 yards apart have spotted a hot air balloon. The angle of elevation from one person to the

Answer 1

Answer:

$h =\sqrt{390.731^2 -152.671^2}=359.670 ft$

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.

$\frac{sin (67)}{h_2} = \frac{sin (67)}{500}$

From this we have that $h_2 = 500$

And for h1 we have this:

$\frac{sin(67)}{500} = \frac{sin(46)}{h_1}$

And we got $h_1 = \frac{sin(46)}{sin(67)} 500= 390.731 ft$

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:

$h^2 + x^2 = h^2_1$  (1)

And for the right triangle we got:

$h^2 +(500-x)^2 = h^2_2$   (2)

We can subctract equation (2) and (1) and we got:

$(500-x)^2 -x^2 = h^2_2 -h^2_1$

And if we apply some algebra we got this:

$250000 -1000 x +x^2 -x^2 = 97329.185$

$250000 -1000 x = 97329.185$

$1000 x = 152670.815$

$x =152.671$

Now since we have the value of x we can find the value for h like this:

$h^2 = h^2_1 -x^2$

$h =\sqrt{390.731^2 -152.671^2}=359.670 ft$