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Answer:
To find the angle of elevation, we can use the tangent function, which relates the opposite side (vertical rise) to the adjacent side (horizontal distance) of a right triangle.
First, convert the horizontal distance from miles to feet:
\[ 2 \text{ miles} = 2 \times 5280 \text{ feet} = 10560 \text{ feet} \]
Next, use the formula for the tangent of the angle \(\theta\):
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{300}{10560} \]
Now, calculate \(\theta\) by taking the arctangent (inverse tangent) of the ratio:
\[ \theta = \tan^{-1} \left( \frac{300}{10560} \right) \]
Using a calculator:
\[ \theta \approx \tan^{-1} (0.0284) \]
\[ \theta \approx 1.63^\circ \]
The closest option is:
b. 1.6°
Answer:
To find the angle of elevation, we can use trigonometry. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the road (300 feet) and the adjacent side is the horizontal distance (2 miles = 2 * 5280 feet).
First, let's convert 2 miles to feet: 2 miles * 5280 feet/mile = 10560 feet.
Now, we have the opposite side (300 feet) and the adjacent side (10560 feet) for the triangle formed by the road and the horizontal line.
The tangent of the angle of elevation (θ) is calculated as:
tan(θ) = opposite/adjacent
tan(θ) = 300/10560
tan(θ) ≈ 0.028409
To find the angle θ, we take the arctan of 0.028409:
θ ≈ arctan(0.028409)
θ ≈ 1.6°
Therefore, the angle of elevation is approximately 1.6°, so the correct option is:
b. 1.6°