Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero. Cotangent is the reciprocal of tangent, so the cotangent of any angle x for which tan x = 0 must be undefined, since it would have a denominator equal to 0. The value of tan (0) is 0, so the cotangent of (0) must be undefined.

Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero. Cosecant is the reciprocal of sine, so the cosecant of any angle x for which sin x = 0 must be undefined, since it would have a denominator equal to 0. The value of sin (0) is 0, so the cosecant of 0 must be undefined.

Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero. Tangent is defined as the ratio between the side length opposite to the angle in question and the side length adjacent to it (TOA, or tan x = opposite/adjacent). In a triangle created by the angle x and the x-axis, the adjacent side length lies along the x-axis; however, when the angle x lies on the y-axis, no length can be drawn along the x-axis to represent the angle. As a result, the denominator of the fraction created by the definition tan x = opposite/adjacent is equal to zero for any angle along the y-axis (90 or 270 degrees, or pi/2 or 3pi/2 in radians.) Therefore, tan 3(pi)/2 is undefined.

Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero. Cosecant is the reciprocal of sine, so the cosecant of any angle x for which sin x = 0 must be undefined, since it would have a denominator equal to 0. The value of sin (pi) is 0, so the cosecant of pi must be undefined.

Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero. Tangent is defined as the ratio between the side length opposite to the angle in question and the side length adjacent to it (TOA, or tan x = opposite/adjacent). In a triangle created by the angle x and the x-axis, the adjacent side length lies along the x-axis; however, when the angle x lies on the y-axis, no length can be drawn along the x-axis to represent the angle. As a result, the denominator of the fraction created by the definition tan x = opposite/adjacent is equal to zero for any angle along the y-axis (90 or 270 degrees, or pi/2 or 3pi/2 in radians.) Therefore, tan (pi)/2 is undefined.

We don't have this triangle's height to use the formula , so we'll need to use trigonometry to find the area of this triangle. We can use the formula , where R is the area of a triangle. This formula comes from the fact that  and also incorporates triangle trigonometry and the Law of Sines. Applying the formula, we get:

We don't have this triangle's height to use the formula , so we'll need to use trigonometry to find the area of this triangle. We can use the formula , where R is the area of a triangle. This formula comes from the fact that  and also incorporates triangle trigonometry and the Law of Sines. Applying the formula, we get:

Since we are not given the height of this triangle, we'll need to use trigonometry to find its area. If you draw and label the triangle, you'll notice that we are given Side-Side-Angle, which is the ambiguous case, and therefore there may be two different values that satisfy . Let's start by finding those.

Use the Law of Sines to find

Because this value is less than 1, there are two values that satisfy . We can now find these using inverse trig and knowing that . We have:

 and 

Because we have two values that satisfy , we'll also have two angles that satisfy , and two unique triangles with two unique areas.  Each of these is found below.

Next, we can use the formula , where R is the area of a triangle. This formula comes from the fact that  and also incorporates triangle trigonometry and the Law of Sines. Applying the formula, we get:

 Now, find  for our second triangle. 

Since we are not given the height of this triangle, we'll need to use trigonometry to find its area. If you draw and label the triangle, you'll notice that we are given Side-Side-Angle, which is the ambiguous case, and therefore there may be two different values that satisfy . Let's start by finding those.

Use the Law of Sines to find

While this is the ambiguous case, there is only one solution if the side opposite the given angle (a=125 ft) is equal to or greater than the other given side (b=95 ft). Because , there is only one value of  and only one solution to this triangle's area. Therefore, we can continue onward to find this triangle's area. 

Next, we can use the formula , where R is the area of a triangle. This formula comes from the fact that  and also incorporates triangle trigonometry and the Law of Sines. Since we know a and b both, we could use either of the first two formulas to find the area. You'll get the same answer either way; feel free to test the other one to see this shown. Applying the formula, we get:

Using the formula for area of a triangle equal to , drawing  and labelling its sides, angles, and height h, then using triangle trigonometry and substitution, we can derive the formulae , where R is equal to area. This can be used to find the area of a triangle when we know two of its sides and the included angle. Plugging in, we get:

Therefore the area of this triangle is 129.2 square inches.