Question

Isaac and Albert spot a hot air balloon flying at a low altitude. They decide to calculate it's height by standing 400 feet apart on a level surface and measuring the angle of elevation to the ballon. From Albert the ballon was at an angle of elevation of 62 degree and from Isaac it was 48 degree. Determine the height h of the ballon above the ground to the nearest foot.

Answer 1

If the heing is h, then

tan 62 = h/x

x = h/1.88

tan 48 = h/(400-x)

400-x = h/1.11

400 - h/1.88 = h/1.11

1.4328h = 400

h = 279.17 m

Answer 2

Answer:

Height of the  ballon above the ground is 279.4 feet .

Step-by-step explanation:

As given

Isaac and Albert spot a hot air balloon flying at a low altitude.

They decide to calculate it's height by standing 400 feet apart on a level surface and measuring the angle of elevation to the ballon.

From Albert the ballon was at an angle of elevation of 62 degree and from Isaac it was 48 degree.

As the diagrams are given below .

Now by using the trignometric identity .

$tan\theta = \frac{Perpendicular}{Hypotenuse}$

As in Δ AOC

$\theta = 48^{\circ}$

AO = h

OC = x

$tan\ 48^{\circ} = \frac{AO}{OC}$

$tan\ 48^{\circ} = \frac{h}{x}$

h = 1.111 × x (Approx)

h = 1.111x

As in Δ AOB

$\theta = 62^{\circ}$

AO = h

OB = 400 - h

$tan\ 62^{\circ} = \frac{AO}{OB}$

$tan\ 62^{\circ} = \frac{h}{400-x}$

h =  1.881 × (400 - x)(Approx)

h = 1.881 (400 - x)

Thus compare the value of h .

1.111x = 1.881 (400 - x)

1.111x = 1.881 × 400 - 1.881x

1.111x + 1.881x = 752.4

2.992x = 752.4

$x = \frac{752.4}{2.992}$

x = 251.5 feet (Approx)

Putting the value of x in the equation

h = 1.111 × 251.5

  = 279.4 feet (Approx)

Therefore the height of the  ballon above the ground is 279.4 feet .