In order to find out who SohCahToa Joe is, we need to find his favorite number from the clues we were given.

The first clue was to find the height of the Taj Mahal, given the angle of elevation of 79.9 degrees, and the adjacent length of 100 feet.

In terms of Sine, Cosine, and Tangent, we are given the adjacent length and the included angle, and need to find the opposite length. To do so, we set up the equation using tangent, because we have "a" and we need "o".

Next, we used the Cross Products Property to isolate the variable SohCahToa Joe gave us, "h".

Lastly, we simplified the value, and rounded to the nearest foot, as SohCahToa Joe said to in his clue.

For clue #2, we had to solve for "m", but to do so we had to solve 3 triangles using the Pythagorean Theorem, because they're all right triangles.

We found the second clue, which is m=21

For the third clue, we had to first find all of the angles for the triangle to determine if any were above 50 degrees.

For the next triangle, we were given "o" and "a" lengths, so to find the included angle we used inverse tangent.

To find the last angle, we again subtracted the two angles that we had from 180.

Two of the angles from the two triangles were over 50 degrees, making the first answer C.

For the next one, we first solved for the first value to figure out what the number was.

Next, we plugged in the choices to figure out which measure matched the first one, and option C did match

Lastly, we drew the triangle the question described.

Then, because we were given the side length for "p", we solved for angle P using the Law of Sines because we were given two sides and an angle measure.

This was option C, and it was true. This concluded that none of the answers were A, so the clue is a=0

For clue 4, we had to find which ramp was the longest, and to do that for the cosine ramp, we used cosine to find the length of both hypotenuses, and then added them together.

To find the length of the Sine ramp, since they were both special right triangles, we used the formula for the 45 45 90 triangle, hypotenuse= side(square root of 2), and for the 30 60 90 triangle, hypotenuse= 2(short side).

The Cosine ramp was longer than the Sine ramp, meaning that J=-5

For clue 5, we first had to find how far the plane traveled in 48 seconds, traveling at 853 feet per second.

For the last clue, we needed to find the length of the bridge. To do that, we first found the third missing angle by subtracting the other two from 180, getting 31 degrees. Then, because we were solving for a side and originally given 2 angles, we used the Law of Sines to solve for the length of the bridge.

This gave us all of the values to solve the formula SohCahToa Joe included in the clues to find his favorite number.

H=561, M=21, A=0, J=-5, T=29029, L=1315

Therefore, SohCahToa Joe is... Carlo.