in the distance you see an arch 192m. you estimate your line of sight with the top of the arch to be 8.4 degrees above the horizontal. appox how far in kilometers are you from the base of the arch?

192 m = 0.192 km

tan 8.4 = 0.192/d

Please indicate the subject where it says "School Subject", NOT the grade level.

To determine the distance from the base of the arch, we can use trigonometry. The angle of elevation (θ) is given as 8.4 degrees, and the height of the arch (h) is given as 192m. We need to find the distance (d) from the base of the arch.

First, we need to express the angle in radians, as trigonometric functions typically work with radians. To convert degrees to radians, we can use the formula: radians = degrees × (π/180).

θ in radians = 8.4 degrees × (π/180) ≈ 0.1464 radians.

Now let's define the trigonometric relationship involved. The tangent function relates the angle of elevation to the sides of a right-angled triangle. We can use the tangent function to find the distance (d).

The tangent of an angle (θ) is equal to the ratio of the opposite side (h) to the adjacent side (d). Therefore, we have the equation: tan(θ) = h / d.

Rearranging the equation to solve for d, we get: d = h / tan(θ).

Plugging in the given values, we have: d = 192m / tan(0.1464) ≈ 1937.8m.

To convert the distance from meters to kilometers, we divide by 1000: d ≈ 1937.8m / 1000 ≈ 1.9378km.

Therefore, you are approximately 1.9378 kilometers away from the base of the arch.