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

question 480

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 $a = 6 , b = 8 , c = 8$ , 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) \(54.40 ^ { \circ }\)

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Definitions:

Normal Model

Another term for a normal distribution, a bell-shaped curve that shows the distribution of data with a specific mean and standard deviation.

Standard Deviation

An index indicating the amount by which individuals within a data set tend to deviate from the average or mean value.

Normal Model

A statistical model that describes data that clusters around a mean in a symmetrical, bell-shaped distribution.

Mean

The average value calculated by adding all numbers in a dataset and dividing by the count of numbers.