Final answer:
To find the value of tan C in a right-angled triangle with sides AB = 24 cm, BC= 7 cm, and a right angle at B, we first find AC using the Pythagorean theorem which yields AC = 25 cm. Then, using the tangent function, tan C equals the length of the opposite side (AB) over the length of the adjacent side (BC), giving us tan C = 24/7.
Step-by-step explanation:
To find the value of tan C for the right-angled triangle ABC, where angle B is 90 degrees, AB = 24 cm, and BC = 7 cm, we can use the definition of the tangent function. Tan C, in a right-angled triangle, is the length of the opposite side to angle C divided by the length of the adjacent side to angle C.
In triangle ABC, AC is the hypotenuse, and since the triangle is right-angled at B, the lengths AB and BC are the legs of the triangle, with BC being the side adjacent to angle C and AB being the side opposite to angle C. Using the Pythagorean theorem (AB^2 + BC^2 = AC^2), we find the length of AC to be:
AC = √(AB^2 + BC^2) = √(24^2 + 7^2) = √(576 + 49) = √625 = 25 cm
Therefore, tan C = (opposite/adjacent) = AB/BC = 24/7.
Hence, the value of tan C is 24/7 or approximately 3.4286.