When driving west toward the Rocky Mountains, you see a peak 3.0 above the horizon. Your GPS gives your current elevation as 1630 , and according to the map, you're 28.5 (horizontally) from the peak.

Find the peak's elevation

What are the units of your 28.5 number? And of your elevation? And the 3.0 ? Is the latter degrees?

You can't do physics without including dimensions with your numbers.

This appears to be basically a trig problem. Use the definition of the tangent of an angle.

Sorry it is 28.5m horizontally from the peak. You see a peak at 3.0 degrees, and the current eleevation is 1630 meters.

Elevation (in meters) = 1630 + 28,500 tan 3.0

= 3124 m

To find the peak's elevation, we can use the concept of trigonometry and the information provided.

First, we can visualize the situation. You are driving west toward the Rocky Mountains, and you see a peak that is 3.0 degrees above the horizon. The GPS gives your current elevation as 1630 units, and you are 28.5 units away from the peak horizontally.

Now, let's break down the problem step by step.

Step 1: Convert the angle from degrees to radians.
Since trigonometric functions typically work with radians, we need to convert the given angle of 3.0 degrees to radians. We can use the formula:

radians = degrees * (π / 180)

Using this formula, we find:
radians = 3.0 * (π / 180) ≈ 0.0523599 radians

Step 2: Determine the change in elevation.
The change in elevation from your current position to the peak can be found using trigonometry. We can use the tangent function:

tan(angle) = opposite / adjacent

In this case, the angle is the converted angle in radians and the opposite side is the unknown change in elevation. The adjacent side is the horizontal distance you are from the peak.

So we have:
tan(0.0523599) = change in elevation / 28.5

Rearranging the equation to solve for the change in elevation:
change in elevation = 28.5 * tan(0.0523599)

Using a calculator, the change in elevation is approximately 1.55 units.

Step 3: Find the peak's elevation.
To find the peak's elevation, we need to add the change in elevation to your current elevation. Therefore:

peak's elevation = current elevation + change in elevation
peak's elevation = 1630 + 1.55
peak's elevation ≈ 1631.55 units

So, the peak's elevation is approximately 1631.55 units.