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

Answer:

x ≈ 31.64

Step-by-step explanation:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

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.

$\implies \sf \tan(36^{\circ})=\dfrac{23}{x}$

$\implies \sf x=\dfrac{23}{\tan(36^{\circ})}$

Substituting the given value for tan 36°:

$\implies \sf x \approx \dfrac{23}{0.727}$

$\implies \sf x\approx31.64$