Explanation:
1.
a right-angled triangle. with the right angle being between the tree and the line of distance of the ranger to the tree.
the angle at the bottom corner, where the ranger is standing, is 63°.
so, the distance line in the ground of 400ft is cos(63) times the length of sight from the ranger to the top of the tree. this line of sight is the Hypotenuse of baseline of the triangle.
400 = cos(63)×baseline
baseline = 400/cos(63) = 881.0757058... ft
and now we can use Pythagoras to calculate the third side (the height of the tree).
baseline² = 400² + tree²
tree² = baseline² - 400² = 776,294.3994... - 160,000 =
= 616,294.3994...
tree = 785.0442022 ft ≈ 785 ft
2.
the left side is 275 ft.
the baseline of Hypotenuse is 325 ft.
we need the angle at the right bottom corner.
the left side 275 is actual sine of that angle times the baseline.
275 = sin(angle)×325
sin(angle) = 275/325 = 0.846153846...
angle = 57.7957725...° ≈ 58°
3.
the right-angled triangle is the distance up in the air of airplane to runway, the current height of the plane, and the line of sight as baseline.
we need the angle in the upper corner at the airplane going down from the high distance line.
we can calculate the length of the baseline via Pythagoras :
4000² + (3×5280)² = baseline²
16,000,000 + 250,905,600 = baseline²
266,905,600 = baseline²
baseline = 16,337.24579... ft
the height 4000ft is the sine of the desired angle of depression times the baseline.
4000 = sin(angle)×baseline
sin(angle) = 4000/ baseline = 0.244839311...
angle = 14.1723377...° ≈ 14°
I have a comment : we should not aim for the end of the HWY. the plane will need a certain distance in the ground to come to a stop. so, we need to aim for 3 miles minus that dissuade needed to stop on the ground.
but we did not get any information for that.