Use vectors to find the measure of the angle at vertex B of triangle ABC,when $A = ( 5,4 )$ , $B = ( - 2,4 )$ ,and $C = ( - 3 , - 4 )$ .Round answer to two decimal places.
A)95.94°
B)98.47°
C)97.13°
D)95.04°
E)99.65°

Question

Quizplus · Accepted Answer

Let's first find vector AB and vector BC:

AB = (0-1)i + (5-5)j + (4-4)k = -i
BC = (4-0)i + (3-5)j + (1-4)k = 4i -2j -3k

Now, we can find the dot product of AB and BC:

AB · BC = |-1| |4| cosθ

cosθ = (AB · BC) / (|AB| |BC|) = (-4) / (√1 √29) = -4/√29

θ = cos⁻¹(-4/√29) ≈ 97.13°

Therefore, the measure of the angle at vertex B is approximately 97.13°, which corresponds to choice C.

Use Vectors to Find the Measure of the Angle at Vertex