Questions: Use the figure below to find the exact value of the trigonometric function of angle A. cot (A)

Solution Steps

In the given right triangle, the lengths of the sides are:

• Opposite side to angle A: 4
• Adjacent side to angle A: 10
• Hypotenuse: Not given directly

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): \[ c^2 = a^2 + b^2 \] \[ c^2 = 4^2 + 10^2 \] \[ c^2 = 16 + 100 \] \[ c^2 = 116 \] \[ c = \sqrt{116} \] \[ c = 2\sqrt{29} \]

The cotangent (cot) of an angle in a right triangle is the ratio of the length of the adjacent side to the length of the opposite side: \[ \cot(A) = \frac{\text{adjacent}}{\text{opposite}} \] \[ \cot(A) = \frac{10}{4} \] \[ \cot(A) = \frac{5}{2} \]

Final Answer