Answer
(a) The angle will be between 5 and 7 degrees, so answer (2)
(b) The average angle would be $6.2^{\circ}$
Work Step by Step
(a) Since the first angle was 5 degrees above the horizontal, and the second angle was 7 degrees above the horizontal, the average angle over the distance must be between those two values.
(b) The average angle can be calculated by breaking down the vertical and horizontal components of each hill, summing them, and then recalculating the net average angle:
Hill 1:
x-component: $x_1 = cos(5^{\circ}) * 2.00 km$
y-component: $y_1 = sin(5^{\circ}) * 2.00 km$
Hill 2:
x-component: $x_2 = cos(7^{\circ}) * 3.00 km$
y-component: $y_2 = sin(7^{\circ}) * 3.00 km$
Total:
x-component: $x_1+x_2= 4.97 km$
y-component: $y_1+y_2= 0.54 km$
Then, use inverse tangent to calculate the average angle:
$tan( \theta ) = \frac{0.54}{4.97}$
$\theta \approx 6.2^{\circ}$
