Final answer:
The angle of elevation to the nearest degree that Kristin is looking at the summit of Pikes Peak is approximately 35°. Since this is not an option and the closest options are 33° or 45°, the nearest degree would be 33°.
Step-by-step explanation:
To find the angle of elevation that Kristin is looking at the summit of Pikes Peak, we can use trigonometric functions. Since Kristin is 2 miles from the base and the summit is 1.4 miles above the base, we can form a right-angled triangle with the horizontal distance as the base, the elevation as the height, and Kristin's line of sight as the hypotenuse.
We'll use the tangent function, which is the ratio of the opposite side (height of the mountain) to the adjacent side (distance from the base). The formula is:
tangent(angle) = opposite/adjacent
Plugging in our values:
tangent(angle) = 1.4 miles / 2 miles
To find the angle, we take the arctangent (inverse tangent) of the ratio:
angle = arctan(0.7)
Using a calculator:
angle ≈> 35 degrees
However, since we need to round to the nearest degree as per the question's requirement, the angle of elevation is approximately 35°. This option is not listed, so the student should re-check the values or the question to ensure they're correct. Our closest options would then be either 33° or 45°, with 33° being the nearest rounded down angle.