𝐴𝐵𝐶𝐷 is a rectangle where the diagonal 𝐴𝐶 is equal to four centimeters and the measure of angle 𝐴𝐶𝐵 is equal to 27 degrees. Find the length of 𝐵𝐶, giving the answer to two decimal places.
We can see from the diagram that the triangle 𝐴𝐵𝐶 is right angled. The length of 𝐴𝐶 is four centimeters and the angle 𝐴𝐶𝐵 is 27 degrees. We want to calculate the length of 𝐵𝐶.
In order to solve this problem, we can use one of the trigonometrical ratios: cos 𝜃 is equal to the adjacent divided by the hypotenuse. Length 𝐴𝐶 is the hypotenuse as it is the longest side and is opposite the right angle. Length 𝐵𝐶 is the adjacent as it is adjacent or next to the 90-degree and 27-degree angles.
Substituting our values into this equation gives us cos of 27 equals 𝑥 divided by four. If we multiply both sides of the equation by four, we are left with 𝑥 is equal to four multiplied by cos 27. Four multiplied by cos 27 is equal to 3.56 to two decimal places.
This means that the length 𝐵𝐶 on the rectangle is 3.56 centimeters.