9514 1404 393
Answer:
-101 feet
Explanation:
The mnemonic SOH CAH TOA reminds you that the relevant relation is ...
Tan = Opposite/Adjacent
Opposite = Adjacent × Tan
height = (0.5 × 5280 ft) × tan(47°) ≈ 2831 ft
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The usual relation between estimates and errors is ...
error = estimate - actual
Then ...
actual = estimate - error
For the given angle and error, the actual angle is ...
actual angle = 47° -(-1°) = 48°
actual height = (2640 ft)·tan(48°) ≈ 2932 ft
Then the change in the height of the mountain due to the error is ...
2831 ft -2932 ft = -101 ft
The error of -1° in angle estimate creates an error of -101 ft in the height estimate.