Question

Solve for z, m and p. Type answers as whole numbers. For example, ifanswer is two type "2"

Answer 1

Finding Z:

`\begin{gathered} \text{ The sum of angles in a triangle is 180\degree} \\ \text{ Thus, we have:} \\ \\ 60\degree+90\degree+\angle Z\degree=180\degree \\ 150\degree+\angle Z=180\degree \\ \text{ Subtract 150 from both sides} \\ \\ \therefore\angle Z=180-150=30\degree \end{gathered}`

Finding P:

`\begin{gathered} \text{ Applying SOHCAHTOA, we have that:} \\ \tan60\degree=(P)/(√(3)) \\ \\ \therefore P=√(3)*\tan60\degree \\ \\ P=√(3)*√(3) \\ \\ P=3 \end{gathered}`

Finding M:

`\begin{gathered} \text{ Applying SOHCAHTOA once more, we have:} \\ \sin Z=(√(3))/(m) \\ \\ \text{ We know Z= 30} \\ \\ \sin30\degree=(√(3))/(m) \\ \\ \text{ We can rewrite this as:} \\ m=(√(3))/(\sin30\degree) \\ \\ \text{ But,} \\ \sin30\degree=(1)/(2) \\ \\ \text{ Thus,} \\ m=(√(3))/((1)/(2))=2√(3) \\ \\ m=2√(3) \end{gathered}`