Part A; The plane will have to travel 70.61 km to fly over the first tower
Part B; The plane will have to travel 5.28 km to fly over the second tower
Step-by-step explanation:
Step 1; Assume the plane is x km away from the control tower. We know it is flying at a height of 3.7 km and an angle of depression of 3°. So a right-angled triangle can be formed using these measurements. The triangle's opposite side measures 3.7 kilometers while the opposite side measures x kilometers. The angle of the triangle is 3°
Step 2; Since we have the length of the opposite side and the angle of the triangle, we can determine the tan of an unknown angle.
tan 3°= [tex]\frac{3.7}{x}[/tex], x = [tex]\frac{3.7}{tan 3}[/tex], tan 3° = 0.0524,
x = 70.6106 kilometers.
So the plane must travel 70.61 km to fly over the first tower.
Step 3; Assume the plane is y km away from the control tower. We know it is flying at a height of 3.7 km and an angle of depression of 35°. So a right-angled triangle can be formed using these measurements. The triangle's opposite side measures 3.7 kilometers while the opposite side measures y kilometers. The angle of the triangle is 35°
Step 4; Since we have the length of the opposite side and the angle of the triangle, we can determine the tan of an unknown angle.
tan 35°= [tex]\frac{3.7}{y}[/tex], y = [tex]\frac{3.7}{tan35}[/tex], tan 35° = 0.7002,
y = 5.2842 kilometers.
So the plane must travel 5.28 km to fly over the second tower.
