Question

What is the approximate value of x in the diagram below

Answer 1

We use Tan in this case:

Tan=(opposite/adjacent)

Tan(36)=23/x

x=23/Tan(36)

x=31.64 length

Hope it helps!

Answer 2

x ≈ 31.64

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 (the side opposite the right angle)

Given:

• sin 36° ≈ 0.588
• cos 36° ≈ 0.809
• tan 36° ≈ 0.727

The given trigonometric ratios all use the angle of 36°.

From inspection of the given diagram:

• x is the side adjacent to the angle of 36°
• 23 is the side opposite to the angle of 36°

Therefore, we should use the tan trig ratio.

`\implies \sf \tan(36^(\circ))=(23)/(x)`

`\implies \sf x=(23)/(\tan(36^(\circ)))`

Substituting the given value for tan 36°:

`\implies \sf x \approx (23)/(0.727)`

`\implies \sf x\approx31.64`