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Given that the measure of angle a is 30 degrees and the length of segment c is 5cm. Fill in the missing measurements

Given That The Measure Of Angle A Is 30 Degrees And The Length Of Segment C Is 5cm Fill In The Missing Measurements class=

Sagot :

Given:

[tex]\begin{gathered} \angle a=30\degree \\ c=5 \end{gathered}[/tex]

Required:

To find the missing information.

Explanation:

Since ABC is a right angle triangle.

[tex]\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 30\degree+90\degree+\angle C=180\degree \\ 120\degree+\angle C=180\degree \\ \angle C=180\degree-120\degree \\ \angle C=60\degree \end{gathered}[/tex]

Now by using the trigonometric ratios we will find the values of a and b.

[tex]\begin{gathered} cos\theta=\frac{adj.}{hyp.} \\ cos30\degree=\frac{5}{b} \\ \frac{\sqrt{3}}{2}=\frac{5}{b} \\ b=\frac{10}{\sqrt{3}} \\ b=\frac{10}{1.732} \\ b=5.77 \\ b\approx5.8 \end{gathered}[/tex]

[tex]\begin{gathered} tan\theta=\frac{opp.}{adj.} \\ tan30\degree=\frac{a}{5} \\ \frac{1}{\sqrt{3}}=\frac{5}{a} \\ a=5\sqrt{3} \\ a=5(1.732) \\ a=8.66 \\ a\approx8.7 \end{gathered}[/tex]

Final answer:

[tex]\begin{gathered} a=8.7 \\ b=5.8 \\ \angle C=60\degree \end{gathered}[/tex]

View image EzmayT788919
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