1 answer
(click or scroll down)
To find the measure of the acute angle of a parallelogram, we can use the formula:
angle = arccos((a^2 + b^2 - c^2) / (2ab))
Where 'a' and 'b' are the lengths of the sides adjacent to the angle, and 'c' is the length of the remaining side.
In this case, the lengths of the sides adjacent to the angle are 32 and 46. The formula becomes:
angle = arccos((32^2 + 46^2 - 46^2) / (2 * 32 * 46))
Simplifying the equation, we have:
angle = arccos((1024 + 2116 - 2116) / (2944))
angle = arccos(1024 / 2944)
Using a calculator or trigonometric tables, we can find the inverse cosine (arccos) of 1024/2944.
Converting this to degrees, we have approximately 71.3 degrees.
Therefore, the measure of the acute angle of the parallelogram to the nearest tenth of a degree is 71.3 degrees.