# Video: Using Right-Angled Triangle Trigonometry to Find Lengths in Rectangles

π΄π΅πΆπ· is a rectangle where the diagonal π΄πΆ = 4 cm and πβ π΄πΆπ΅ = 27Β°. Find the length of segment line π΅πΆ giving the answer to two decimal places.

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### Video Transcript

π΄π΅πΆπ· is a rectangle where the diagonal π΄πΆ is equal to four centimeters and the measure of angle π΄πΆπ΅ is equal to 27 degrees. Find the length of π΅πΆ, giving the answer to two decimal places.

We can see from the diagram that the triangle π΄π΅πΆ is right angled. The length of π΄πΆ is four centimeters and the angle π΄πΆπ΅ is 27 degrees. We want to calculate the length of π΅πΆ.

In order to solve this problem, we can use one of the trigonometrical ratios: cos π is equal to the adjacent divided by the hypotenuse. Length π΄πΆ is the hypotenuse as it is the longest side and is opposite the right angle. Length π΅πΆ 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 π₯ divided by four. If we multiply both sides of the equation by four, we are left with π₯ 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 π΅πΆ on the rectangle is 3.56 centimeters.