Questions: Find (x). Give your answer as an exact value in terms of trigonometric functions. NOTE: The triangle is NOT drawn to scale.

Solution Steps

Let 'a' be the length of the side adjacent to the 1.2 rad angle.

Since we know the length of the opposite side (87) and the angle (1.2 rad), we can use the tangent function.

tan(1.2 rad) = opposite / adjacent = 87 / a

a = 87 / tan(1.2 rad)

Let 'b' be the length of the adjacent side to the 0.2 rad angle.

Since this is the same triangle, we already found that the opposite side is 87. The angle is 0.2 rad.

tan(0.2 rad) = opposite / adjacent = 87 / b

b = 87 / tan(0.2 rad)

x is the difference between the longer adjacent side and the shorter adjacent side.

x = b - a

x = (87 / tan(0.2 rad)) - (87 / tan(1.2 rad))

Final Answer: The exact value of x is 87 / tan(0.2 rad) - 87 / tan(1.2 rad) or 87(1/tan(0.2 rad) - 1/tan(1.2 rad)).