Use vectors to find the measure of the angle at vertex B of triangle ABC, when , , and .Round answer to two decimal places.
A)69.48°
B)71.57°
C)72.91°
D)70.38°
E)74.09°

Question

Use vectors to find the measure of the angle at vertex B of triangle ABC, when  ,  , and  .Round answer to two decimal places.
A)69.48° 
B)71.57° 
C)72.91° 
D)70.38° 
E)74.09°

Quizplus · Accepted Answer

We can use dot product to find the angle at vertex B.

Let AB = vector u = (11eacce6_1f15_867f_9f49_5fedbb359222_TB7896_11 - 11eacce6_1f15_8681_9f49_755e01ae64f5_TB7896_11) = (-4, 5), 
BC = vector v = (11eacce6_1f15_8680_9f49_232f03e32c00_TB7896_11 - 11eacce6_1f15_8681_9f49_755e01ae64f5_TB7896_11) = (5, -3).

Then, we can find cos(B) as the dot product of u and v divided by the product of their magnitudes:

cos(B) = (u · v) / (|u| * |v|) = (-4*5 + 5*(-3)) / (√(16+25) * √(25+9)) = -23 / (21√2)

Finally, we can find the angle B as the inverse cosine of cos(B):

B = cos⁻¹(-23 / (21√2)) ≈ 71.57°

Therefore, the answer is B)71.57°.

Use Vectors to Find the Measure of the Angle at Vertex