In a right triangle, CT = 6, CA = 3, and m<CAT = 90. What is the value of cot C ?
CT= hypo
CA= Opp.
AT = √(36-9) = 3√3
cotC = adj/opp = CA/AT = 3/3√3 = 1/√3
you will note that for the side opposite to angle C, point C cannot be one of the endpoints.
To find the value of cot C in a right triangle, we first need to understand what cot C represents. In trigonometry, cot C is the ratio of the adjacent side to the opposite side of angle C in a right triangle.
Given that CT is the hypotenuse (the side opposite the right angle) and CA is the opposite side of angle C, we can determine the adjacent side by using the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse.
Using this theorem, we can find the value of the adjacent side as follows:
AC^2 + CA^2 = CT^2
AC^2 + 3^2 = 6^2
AC^2 + 9 = 36
AC^2 = 36 - 9
AC^2 = 27
AC = sqrt(27)
AC = 3√3
Now that we have the lengths of the adjacent side (AC) and the opposite side (CA), we can calculate the value of cot C. Cotangent is the ratio of the adjacent side to the opposite side, so we divide the length of AC by the length of CA:
cot C = AC / CA
= (3√3) / 3
= √3
Therefore, the value of cot C is √3.