Question

How can I solve this?
Please use the simplest format​

Answer 1

option D is true.

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

• opposite = 4

• adjacent = n

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

`m=\sqrt{\left(4\cdot (√(3))/(3)\right)^2+4^2}`

`m=\sqrt{(4^2)/(3)+4^2}`

`m=\sqrt{(64)/(3)}`

`m=(8)/(√(3))`

`m=(8√(3))/(3)`

Thus,

• 
  `m=(8√(3))/(3)`

• n = 4√3 / 3

Therefore, option D is true.