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 th
at 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.
1 answer:
Answer: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
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In order to find out the answer to this question, we can distribute
Flip your problem around!
Add by
Like:
Cancel out:
Keep:
Your problem becomes:
Now, we have to divide by
Like:
Cancel:
Keep:
Good luck on your assignment and enjoy your day!
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