Solve the Problem $( a , b )$ And (C, D) Be Two Points in the First Quadrant

Solve the problem.
-Let $( a , b )$ and (c, d) be two points in the first quadrant, and let $\theta$ be the angle between the line segment connecting $( a , b )$ with the origin and the line segment connecting $( c , d )$ with the origin. It can be shown that
$\cos \theta = \frac { a c + b d } { \sqrt { \left( a ^ { 2 } + b ^ { 2 } \right) \left( c ^ { 2 } + d ^ { 2 } \right) } }$
Find $\theta$ if $a = 6 , b = 8 , c = 8$ , and $d = 2$ . Give your answer in degrees rounded to the nearest hundredth.

A) $67.17 ^ { \circ }$
B) $78.81 ^ { \circ }$
C) $39.09 ^ { \circ }$
D) $54.40 ^ { \circ }$

Correct Answer:

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