in the distance you see an arch 192 meters high, you estimate your line of sight with the top of the arch to be 8.4 degree. appox how far in kilometers are you from the base of the arch?
tan8.4-0.192/d? is this the complete answer?
Damon answered your question and even gave you the equation to solve.
tan 8.4 = 0.192/d
was that equation, not what you typed above.
Your question is based on trigonometry. If you are studying trig, then surely you must have learned how to solve simple equations.
To find the distance in kilometers from the base of the arch, you can use the tangent function and a little trigonometry.
The tangent function relates the angle of elevation (8.4 degrees) to the opposite side of a right triangle (the height of the arch, 192 meters) and the adjacent side (the distance from the base of the arch).
Let's break down the equation step-by-step:
1. Start with the formula for tangent: tan(angle) = opposite/adjacent.
2. Substitute the known values: tan(8.4 degrees) = 192 meters/distance.
3. Rearrange the equation to solve for distance: distance = 192 meters / tan(8.4 degrees).
4. Convert the result to kilometers: Since the distance was given in meters, divide the result by 1000 to convert it to kilometers.
So, the complete answer would be:
Distance = 192 / tan(8.4 degrees) kilometers.