Solve the Problem $( a , b )$ And $( c , d )$

Multiple Choice

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 $a = 7 , b = 5 , c = 2$ , and $d = 8$ . Give your answer in degrees rounded to the nearest hundredth.

A) $111.50 ^ { \circ }$
B) $40.43 ^ { \circ }$
C) $55.68 ^ { \circ }$
D) $78.62 ^ { \circ }$