Question

In a triangle where b = 4.95 m at 60.0°, c and a have equal magnitudes. The direction angle of c is larger than that of a by 25.0°. If a · b = 29.1 m² and b · c = 32.1 m², find the magnitude (in m) and direction (in degrees) of a.

a) Magnitude: 17.3, Direction: 30.0°
b) Magnitude: 20.1, Direction: 75.0°
c) Magnitude: 15.5, Direction: 105.0°
d) Magnitude: 22.8, Direction: 85.0°

Answer 1

To find the magnitude and direction of vector a in a triangle, we use the dot product formula and solve for the magnitude of c. Then, since the magnitude of a is equal to the magnitude of c, we find the direction of a.

Thus, the correct option is A.

Step-by-step explanation:

To find the magnitude and direction of vector a in the given triangle, we can use the dot product formula. Let's start by finding the magnitude of vector c.

Using the magnitude of vector b (4.95 m) and the dot product of vectors b and c (32.1 m²), we can use the formula |b||c|cosθ to find the magnitude of c. Solving for |c|, we get: |c|= √(b · c / cosθ) = √(32.1 / cos60°) = 6.05 m.

Now, since the magnitude of a is equal to the magnitude of c, we can conclude that |a| = 6.05 m.

The direction of vector c is larger than that of a by 25°, so the direction of a is 60° - 25° = 35°.