Answer:
∠S = 21.10°
∠M = 79.45°
PM = 9.16
Step-by-step explanation:
Here Pythagorean theorem and trigonometry suffice to solve our problem.
From the Pythagorean theorem we get:
[tex]KM^2+9^2=PM^2[/tex] and
[tex](25-KM)^2+9^2=25^2.[/tex]
We solve for [tex]KM[/tex] in the second equation and get:
[tex](25-KM)=\sqrt{25^2-9^2}[/tex]
[tex]\therefore KM=25-\sqrt{25^2-9^2} =\boxed{1.68}[/tex]
Now since
[tex]SK+KM=25\\\\ SK=\boxed{23.32}[/tex]
Therefore
[tex]{\angle}S=Tan^{-1}(\frac{PK}{SK}) = Tan^{-1}(\frac{9}{23.32})=21.10^o[/tex]
and
[tex]{\angle}M=Tan^{-1}(\frac{PK}{KM}) = Tan^{-1}(\frac{9}{1.68})=79.45^o.[/tex]
And finally again from the Pythagorean theorem:
[tex]PM^2=PK^2+KM^2=9^2+1.68^2[/tex]
[tex]\therefore PM=\sqrt{9^2+1.68^2} =9.16.[/tex]
Thus,
∠S = 21.10°
∠M = 79.45°
PM = 9.16.
