jessica is standing 2 miles from the center of the base of pikes peak and looking at the summit of the mountain which is 1.4 miles from the base, what angle of elevation is jessica looking at the summit of the mountain?

tan x = 1.4/2

x = 35 degrees

To find the angle of elevation that Jessica is looking at the summit of the mountain, we can use basic trigonometry.

Let's assume that Jessica and the summit of the mountain form a right triangle, with Jessica's position as the base of the triangle, the line connecting her position to the summit as the hypotenuse, and a perpendicular line from Jessica's position to the summit as the height (opposite side).

Now, we know that Jessica is standing 2 miles from the center of the base of Pikes Peak, and the summit of the mountain is 1.4 miles from the base. Therefore, the base of the right triangle is 2 miles long, and the hypotenuse is 1.4 miles long.

Using the trigonometric function tangent (tan), we can find the angle of elevation, which is the angle between the base and the hypotenuse.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height (the distance from Jessica's position to the summit), and the adjacent side is the base (the distance from Jessica's position to the center of the base).

So, we can calculate the angle of elevation as:

angle of elevation = arctan(opposite/adjacent)

angle of elevation = arctan(1.4/2)

Using a calculator or trigonometric table, we can find the arctan of the ratio 1.4/2, which is approximately 33.69 degrees.

Therefore, Jessica is looking at the summit of Pikes Peak at an angle of elevation of approximately 33.69 degrees.

To find the angle of elevation, we can use trigonometry. The tangent of the angle of elevation is equal to the opposite side divided by the adjacent side.

In this case, Jessica is looking at the summit of the mountain, which is the opposite side. The distance from the center of the base to the summit is the hypotenuse, and the distance from Jessica to the center of the base is the adjacent side.

Let's denote:
Opposite side = x (distance from Jessica to the summit)
Adjacent side = 2 miles (distance from Jessica to the center of the base)

Using the Pythagorean theorem, we can find the value of the opposite side (x):
x^2 = (2 miles)^2 + (1.4 miles)^2
x^2 = 4 + 1.96
x^2 = 5.96
x ≈ √5.96
x ≈ 2.44 miles

Now, we can calculate the tangent of the angle of elevation:
tan(angle of elevation) = opposite/adjacent
tan(angle of elevation) = 2.44 miles/2 miles

To find the angle of elevation, we can calculate the arctan (inverse tangent) of the ratio:
angle of elevation = arctan(2.44 miles/2 miles)

Using a calculator, we find that the angle of elevation is approximately 53.13 degrees.

Therefore, Jessica is looking at the summit of the mountain at an angle of elevation of approximately 53.13 degrees.