Answer:
tan(X) = 4/3 and tan(Z) = 3/4
Step-by-step explanation:
* Lets revise the trigonometry functions
- In any right angle triangle:
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
- For angle A
# sin(A) = opposite/hypotenuse
∵ The opposite to ∠A is BC
∵ The hypotenuse is AC
∴ sin(A) = BC/AC
# cos(A) = adjacent/hypotenuse
∵ The adjacent to ∠A is AB
∵ The hypotenuse is AC
∴ cos(A) = AB/AC
# tan(A) = opposite/adjacent
∵ The opposite to ∠A is BC
∵ The adjacent to ∠A is AB
∴ tan(A) = BC/AB
* Now lets solve the problem
- In Δ XYZ
∵ m∠Y = 90°
∵ XY = 3 inches , YZ = 4 inches , XZ = 5 inches
∴ The hypotenuse is XZ
∴ The legs of the right angle are XY and YZ
* To find tan(X) use YZ as opposite to it and XY as adjacent to it
∵ tan(X) = YZ/XY ⇒ opposite/adjacent
∴ tan(X) = 4/3
* To find tan(Z) use YX as opposite to it and ZY as adjacent to it
∵ tan(Z) = YX/ZY ⇒ opposite/adjacent
∴ tan(Z) = 3/4
* tan(X) = 4/3 and tan(Z) = 3/4
