Answer:
[tex]m = 5 \sqrt{3}[/tex]
[tex]n = 5[/tex]
Step-by-step explanation:
Given
The triangle above
Required
Find the missing lengths
The missing lengths can be calculated by applying trigonometry ratios
From the triangle above,
the Hypotenuse is 10
Angle = 60
Calculating m
The relationship between m, the Hypotenuse and angle 60 is defined as follows;
[tex]sin \theta = \frac{Opp}{Hyp}[/tex]
Where [tex]\theta = 60[/tex]
[tex]Opp = m[/tex]
[tex]Hyp = 10[/tex]
The above formula becomes
[tex]sin60= \frac{m}{10}[/tex]
Multiply both sides by 10
[tex]10 * sin60= \frac{m}{10} * 10[/tex]
[tex]10 * sin60= m[/tex]
In radical from, [tex]sin60 = \frac{\sqrt{3}}{2}[/tex]
[tex]10 * sin60= m[/tex] becomes
[tex]10 * \frac{\sqrt{3}}{2}= m[/tex]
[tex]\frac{10* \sqrt{3}}{2}= m[/tex]
[tex]5 \sqrt{3}= m[/tex]
[tex]m = 5 \sqrt{3}[/tex]
Calculating n
The relationship between n, the Hypotenuse and angle 60 is defined as follows;
[tex]cos\theta = \frac{Adj}{Hyp}[/tex]
Where [tex]\theta = 60[/tex]
[tex]Adj = n[/tex]
[tex]Hyp = 10[/tex]
The above formula becomes
[tex]cos60= \frac{n}{10}[/tex]
Multiply both sides by 10
[tex]10 * cos60= \frac{n}{10} * 10[/tex]
[tex]10 * cos60= n[/tex]
In radical from, [tex]cos60= \frac{1}{2}[/tex]
[tex]10 * cos60= n[/tex] becomes
[tex]10 * \frac{1}{2}= n[/tex]
[tex]\frac{10*1}{2}= n[/tex]
[tex]5 = n[/tex]
[tex]n = 5[/tex]
