The distance from point Y to the flag post measures 38.13 m. Step-by-step explanation: Assuming point Y is located at the intersection of both lines shown. Point X is positioned 34 meters east of point Y. The flagpole at point X is observed at a bearing of N18°W, meaning it creates an angle of 18° to the west from the north at point X. Conversely, at point Y, the flagpole has a bearing of N40°E, which makes a 40° angle towards the east from the north.
Considering ∆ AXY as a right triangle, the angle FXY is established. Then, concerning ∆ BYX as another right triangle, the angle FYX is also determined. To find the third angle ∠YFX in triangle FYX, the angle sum property of triangles can be applied:
∠YFX + ∠FYX + ∠FXY = 180°
Thus, we have: ∠YFX + 50° + 72° = 180° leading to ∠YFX = 58°.
Now we can calculate the distance FY using the sine rule.
The potential values for y areinfinite
Further clarification
Trigonometry is a branch of math focused on the connections between the sides and angles of triangles.
Considering special angles of trigonometric functions, for instance
In the equation y = cos⁻¹ 0, the value of y can be derived as follows:
y = cos⁻¹0
y = arc cos 0
cos y = 0
Thus, the resulting value of y:
Alternatively, it can be expressed as:
⇒ y: arithmetic sequence
So there are infinite solutions for y
Learn more
trigonometric identities
Keywords: trigonometric, infinite values,arithmetic sequence
Answer:
x = -4/45
Step-by-step breakdown:
180x=2(30÷3)+17-5•11+2÷1
We first need to simplify the right side. The initial step involves the parentheses
180x=2(10)+17-5•11+2÷1
Next, we multiply and divide, proceeding from left to right after the equals sign.
180x=20+17-5•11+2÷1
180x=20+17-55+2÷1
180x=20+17-55+2
Next, we add and subtract, moving from left to right in relation to the equals sign.
180x=37-55+2
180x =-18+2
180x = -16
Then divide each side by 180
180x/180 = -16/180
x = -4/45
