When driving west toward the Rocky Mountains, you see a peak 2.6 ∘ above the horizon. Your GPS gives your current elevation as 1490 m , and according to the map, you're 25.0 km (horizontally) from the peak.
Find the peak's elevation.
I thought it would be 1490+25000=26490
26490 tan(2.6)= 15936
1490 + 25,000 tan 2.6 = h
h = 1490 + 1135
h = 2625 meters
how do you get the 1135? I must not be calculating something correct
To find the peak's elevation, we need to use the concept of trigonometry. We can use the tangent function to relate the angle of elevation to the vertical and horizontal distances.
First, let's convert the given angle of 2.6° to radians:
2.6° * (π/180°) ≈ 0.0453 radians
We can then use the tangent function to relate the angle of elevation to the vertical and horizontal distances:
tan(angle) = vertical distance / horizontal distance
In this case, the horizontal distance is given as 25.0 km (or 25000 m), and the angle of elevation is 0.0453 radians. We can rewrite the equation as:
tan(0.0453) = vertical distance / 25000
Now, rearrange the equation to solve for the vertical distance:
vertical distance = tan(0.0453) * 25000
Using a scientific calculator or computer software, we can evaluate the expression:
vertical distance ≈ 26.17 m
Finally, to find the peak's elevation, add the vertical distance to the given GPS elevation:
peak's elevation = 1490 m + 26.17 m ≈ 1516.17 m
So, the peak's elevation is approximately 1516.17 m.