Aboat travels 30 miles north, 20 miles east and 40 miles northeast. what is the angle of rotation of the boats direction from start to finish

The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.

Step-by-step explanation:

Let x axis be east direction and x axis be north direction.

The boat first travels 30 miles north

⇒ Displacement = 30 j

Then boat travels 20 miles east

⇒ Displacement = 20 i

And at last the boat travels 40 miles north east

⇒ Displacement = 40·cos 45 i + 40·sin 45 j

                            = 28.28 i + 28.28 j

Total displacement = 48.28 i + 58.28 j

⇒ θ = 50.36⁰

Hence, The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

answer: your answer is a