Answer:
The ratio [tex]\frac{3}{4}[/tex] represents the tangent of ∠I
Step-by-step explanation:
Let us revise the trigonometry ratio
- sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]
- cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex]
- tan Ф = [tex]\frac{opposite}{adjacent}[/tex]
In Δ HIJ
∵ m∠J = 90°
- Hypotenuse is the side which opposite to the right angle
∴ HI is the hypotenuse
∵ HJ = 3 units
∵ IH = 5 units
- Let us use Pythagoras Theorem to find HJ
∵ (HJ)² + (IJ)² = (IH)²
∴ 3² + (IJ)² = 5²
∴ 9 + (IJ)² = 25
- Subtract 9 from both sides
∴ (IJ)² = 16
- take √ for both sides
∴ IJ = 4 units
To find the tangent of ∠I find the opposite and adjacent sides to it
∵ HJ is opposite to ∠I
∵ IJ is adjacent to ∠I
- use the rule of tan above
∴ tan(∠I) = [tex]\frac{HJ}{IJ}[/tex]
∴ tan(∠I) = [tex]\frac{3}{4}[/tex]
The ratio [tex]\frac{3}{4}[/tex] represents the tangent of ∠I
