Question

Consider this right triangle.

Enter the measure of ZM to the nearest degree.

Answer 1

21°

Explanation:

For this right-angled triangle:

∠M = angle in question

Side LM = Hypotenuse

With respect to ∠M:

Side LN = Opposite side

Side MN = Adjacent side

Trigonometric function applied:

sin∠M =
`(opposite)/(hypotenuse)`

=
`(8)/(22)`

∠M =
`sin^(-1) ((8)/(22))`

= 21.32°

∠M = 21° (Rounded to the nearest degree)

Answer 2

∠M = 21°

Explanation:

`\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

From inspection of the given right triangle:

• The angle to be found is M ⇒ θ = M
• The side opposite ∠M is LN ⇒ O = 8
• The hypotenuse is LM ⇒ H = 22

Therefore, substitute the given values into the sine ratio and solve for ∠M:

`\implies \sin(M)=(8)/(22)`

`\implies M=\arcsin \left((8)/(22)\right)`

`\implies M=21.323686...^(\circ)`

`\implies M=21^(\circ)\sf\;(nearest\;degree)`

Therefore, the measure of ∠M to the nearest degree is 21°.