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Whose good at Geomtry, specifically trigonometry?!!?
Need help really fast, please! An airplane at a constant altitude of 2 miles flies a horizontal towards you at a constant velocity. At the start of your observation, the angle of elevation is 40 degrees. Fifteen seconds later, the angle of elevation is 50 degrees. What is the approximate velocity of the airplaine in miles per minute
A. 0.1 miles per minute
B. 0.7 miles per minute
C. 2.8 miles per minute
D. 10.6 minute

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sqdancefan

Answer:

C. 2.8 miles per minute

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

... Tan = Opposite/Adjacent

In the relevant triangle, the side opposite the angle at the observer is the altitude of the airplane, 2 miles. The side adjacent is the horizontal distance to the airplane. At the first observation, that distance (d1) is ...

... tan(40°) = (2 mi)/d1

At the second observation, the horizontal distance to the airplane (d2) is ...

... tan(50°) = (2 mi)/d2

Solving for d1 and d2 and finding the difference (∆d), we have ...

... d1 = (2 mi)/tan(40°)

... d2 = (2 mi)/tan(50°)

... ∆d = d1 -d2 = (2 mi)(1/tan(40°) -1/tan(50°) ≈ 2·(1.1918 -0.8391) mi

... ∆d ≈ 2°0.3526 mi ≈ 0.7053 mi

This distance was flown by the plane in 15 seconds, so it will travel 4 times this distance in 60 seconds (1 minute).

... ∆d/∆t = (0.7053 mi)/(1/4 min) = 4·0.7053 mi/min ≈ 2.8 mi/min

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