Answer:
option D is true.
Step-by-step explanation:
The right-angled triangle is shown.
From the right-angled triangle,
The angle Ф = 60°
We know that the trigonometric ratio
tan Ф = opposite / adjacent
Thus,
tan 60 = 4 / n
√3 = 4/n
n = 4/√3
Thus,
n = 4/√3
= (4 × √3) / (√3 × √3)
= 4√3 / 3
Thus,
n = 4√3 / 3
Using Pythagorean theorem
m = √n²+4²
[tex]m=\sqrt{\left(4\cdot \frac{\sqrt{3}}{3}\right)^2+4^2}[/tex]
[tex]m=\sqrt{\frac{4^2}{3}+4^2}[/tex]
[tex]m=\sqrt{\frac{64}{3}}[/tex]
[tex]m=\frac{8}{\sqrt{3}}[/tex]
[tex]m=\frac{8\sqrt{3}}{3}[/tex]
Thus,
- [tex]m=\frac{8\sqrt{3}}{3}[/tex]
Therefore, option D is true.
