Question

What is the value of tan x? 3/5 5/4 3/4 4/3 4/5

Answer 1

`\\ \rm\Rrightarrow tanx=(Perpendicular)/(Base)`

• Perpendicular=8
• Base=6

`\\ \rm\Rrightarrow tanx=(8)/(6)`

`\\ \rm\Rrightarrow tanx=(4)/(3)`

Answer 2

`\sf \tan(x)=(4)/(3)`

Explanation:

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle
• H is the hypotenuse (side opposite the right angle)

From inspection of the diagram:

• 
  `\theta` = x
• O = 8
• A = 6
• H = 10

`\implies \sf \tan(x)=(8)/(6)=(4)/(3)`