Complete the table by solving the parallelogram shown in the figure in the website link below. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.)
www.webassign.net/larpcalclim2/6-2-021.gif
a=22
b=39
c=
d=
θ=58 °
ϕ=122°
You are welcome.
To solve the parallelogram and find the lengths of the diagonals, we can use the properties of parallelograms. Here's what we can do step by step:
Step 1: Label the given information in the parallelogram as shown in the figure.
Given:
Length of one side: a = 22
Length of adjacent side: b = 39
Measure of one angle, θ = 58°
Measure of another angle, ϕ = 122°
Step 2: Use the properties of parallel lines to find the length of the diagonals.
The diagonals of a parallelogram bisect each other. Therefore, we can find the length of each diagonal (c and d) by dividing the length of the long side (39) and the short side (22) by 2.
c = (39 / 2) = 19.5
d = (22 / 2) = 11
Step 3: Given that one of the interior angles is 58°, use the angle properties of parallelograms to find the other interior angle.
The opposite interior angles of a parallelogram are congruent. Therefore, we can use the angle θ (58°) to find the other interior angle.
Opposite interior angle = 180° - θ
Opposite interior angle = 180° - 58°
Opposite interior angle = 122°
After completing these steps, the values for c and d are:
c = 19.5
d = 11
Therefore, the complete table would look like this:
______________________
| a | b | c | d |
-----------------------
|22|39|19.5|11|
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this is a repost of my old post.
c and d are wrong in my online assignment
law of cosines
c^2 = a^2 + b^2 - 2 a b cos 122
d^2 = a^2 + b^2 - 2 a b cos 58