To find the angle of elevation of the ramp, we can use the tangent function, which relates the angle of elevation to the opposite side and the adjacent side of the right triangle formed by the ramp.
In this scenario:
- The opposite side is the rise of the ramp: \( h = 1.5 \) meters.
- The adjacent side is the horizontal distance: \( d = 6 \) meters.
The formula for the tangent of the angle \( \theta \) is given by:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d} \]
Substituting in the values:
\[ \tan(\theta) = \frac{1.5}{6} \]
\[ \tan(\theta) = 0.25 \]
To find the angle \( \theta \), we take the arctangent (inverse tangent) of \( 0.25 \):
\[ \theta = \tan^{-1}(0.25) \]
Calculating this using a calculator:
\[ \theta \approx 14.04^\circ \]
Therefore, the angle of elevation of the ramp is approximately \( 14.04^\circ \).
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