Answer:
The value of x is 2.5 to the nearest tenth
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
∵ x is opposite to the angle of measure 23°
∵ 6 is adjacent to the angle of measure 23°
∴ tan(23°) = x/6 ⇒ × 6 to both sides
∴ x = 6 × tan(23°) = 2.5
* The value of x is 2.5 to the nearest tenth
