Question

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

Answer 1

Given:

`\begin{gathered} \angle a=30\degree \\ c=5 \end{gathered}`

Required:

To find the missing information.

Step-by-step explanation:

Since ABC is a right angle triangle.

`\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}`

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

`\begin{gathered} cos\theta=(adj.)/(hyp.) \\ cos30\degree=(5)/(b) \\ (√(3))/(2)=(5)/(b) \\ b=(10)/(√(3)) \\ b=(10)/(1.732) \\ b=5.77 \\ b\approx5.8 \end{gathered}`

`\begin{gathered} tan\theta=(opp.)/(adj.) \\ tan30\degree=(a)/(5) \\ (1)/(√(3))=(5)/(a) \\ a=5√(3) \\ a=5(1.732) \\ a=8.66 \\ a\approx8.7 \end{gathered}`

Final answer:

`\begin{gathered} a=8.7 \\ b=5.8 \\ \angle C=60\degree \end{gathered}`