The value of Tan B × Cos C ÷ Sin C + Cos B for the Isosceles trapezium ABCD is equal to 9/5.
An Isosceles trapezium have equal base angles and therefore the left and right side lengths are also equal. For the Isosceles trapezium ABCD such that AD is parallel to BC , AD = 4cm, AB = 5cm and BC = 12cm, we can get two same right triangles with hypotenuse 5cm and base len asgth 4cm so that the vertical length by Pythagoras is:
√(5² - 4²) = 3
Cos B = 4/5 {adjacent/hypotenuse} and
Tan B = 3/4 {opposite/adjacent}
For the other triangle;
Sin C = 3/5 {opposite/hypotenuse}
Cos C = 4/5 {adjacent/hypotenuse}
Cos C ÷ Sin C = 4/5 × 5/3 = 4/3
Tan B × Cos C ÷ Sin C = 3/4 × 4/3 = 1
Tan B × Cos C ÷ Sin C + Cos B = 1 + 4/5 = 9/5
Therefore, by evaluation the expression Tan B × Cos C ÷ Sin C + Cos B is equal to 9/5.