The length of CD is 8.5
Explanation:
The image of the triangle CDE with the measurements DE=10 , CE=5 , and m∠E=58 is attached below:
To determine the length of CD, let us use the law of cosine formula.
Thus, we have,
[tex]c^{2}=a^{2}+b^{2}-2 a b \cdot \cos (c)[/tex]
where [tex]a=10[/tex] , [tex]b=5[/tex] and [tex]c=58^{\circ}[/tex]
Substituting these values in the above formula, we get,
[tex]c^{2}=(10)^{2}+(5)^{2}-2 (10)(5) \cdot \cos (58)[/tex]
Simplifying,we get,
[tex]c^{2}=100+25-100(0.53)[/tex]
[tex]c^{2}=125-53[/tex]
Subtracting, we get,
[tex]c^{2}=72[/tex]
Taking square root on both sides, we get,
[tex]c=8.5[/tex]
Hence, the length of CD is 8.5
