Answer:
1) angle ABC = 80°
angle ACB = 40°
2) extra distance traveled = 122 km
Step-by-step explanation:
From the image, angle p° will be equal to 60° (alternate angles).
Angle t° will be equal to (90 - 60) = 30°.
Angle r° = (320 - 270) = 50°
Therefore angle ABC = angle (r° + t°) = (50 + 30) = 80°
BCD is a right angle triangle, therefore, the two other angles apart from the right angle must sum up to 90°.
BCD = ACB = (90 - 50) = 40°
lenght of DB is calculated as
sin 60 = DB/150
0.866 = DB/150
DB = 0.866 X 150 = 129.9 km
AD^2 = 150^2 - 129.9^2 = 5625.99 km
AD = 75 km
Tan 50 = CD/129.9
1.192 =CD/129.9
CD = 129.9 X 1.192 = 154.84 km
BC^2 = 154.84^2 + 129.9^ = 40849.44
BC = 202.11 km
If the plane had flown due north it would have covered AD + CD = 75 + 154.84 = 229.84 km
The divertion took a total distance of AB + BC = 150 + 202.11 = 352.11 km
The extra distance is 352.11 - 229.84 = 122.27 km
Approximately 122 km
