While taking a ride in a hot-air balloon in napa valley, francisco wonders how high he is. to find out, he chooses a landmark that is to the east of the balloon and measures the angle of depression to be 54degrees. a few minutes later, after traveling 100 feet east, the angle of depression to the same landmark is determined to be 61degrees. use this information to determine the height of the balloon.

the height of the balloon is 670.244 feet

Step-by-step explanation:

The right angle triangle BLD represents the scenario.

h represents the height of the balloon.

We would apply trigonometric ratio to determine h.

Tan # = opposite side/adjacent side

Looking at triangle LCD,

# = 61 degrees

h = opposite side

x = adjacent side

Tan 61 = h/x

1.7321 = h/x

h = 1.7321x

Looking at triangle LBD,

# = 54 degrees

h = opposite side

x + 100 = adjacent side

Tan 54 = h/x + 100

1.3764 = h/x + 100

h = 1.3764(x + 100)

Therefore,

1.7321x = 1.3764(x + 100)

1.7321x = 1.3764x + 137.64

137.64 = 1.7321x - 1.3764x

137.64 = 0.3557x

x = 137.64/0.3557 = 386.955

h = 1.7321x = 386.955 × 1.7321

h = 670.244 feet