Question

Given:

∆SPM, PK⊥ SM

SP = 25, SM = 28, PK = 9

Find: m∠S, m∠M, PM

Answer 1

∠S = 21.10°

∠M = 79.45°

PM = 9.16

Explanation:

Here Pythagorean theorem and trigonometry suffice to solve our problem.

From the Pythagorean theorem we get:

`KM^2+9^2=PM^2` and

`(25-KM)^2+9^2=25^2.`

We solve for
`KM` in the second equation and get:

`(25-KM)=√(25^2-9^2)`

`\therefore KM=25-√(25^2-9^2) =\boxed{1.68}`

Now since

`SK+KM=25\\\\ SK=\boxed{23.32}`

Therefore

`{\angle}S=Tan^(-1)((PK)/(SK)) = Tan^(-1)((9)/(23.32))=21.10^o`

and

`{\angle}M=Tan^(-1)((PK)/(KM)) = Tan^(-1)((9)/(1.68))=79.45^o.`

And finally again from the Pythagorean theorem:

`PM^2=PK^2+KM^2=9^2+1.68^2`

`\therefore PM=√(9^2+1.68^2) =9.16.`

Thus,

∠S = 21.10°

∠M = 79.45°

PM = 9.16.