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

A swimming pool is in the shape of a trapezoid. Find the length of one of the equal sides giving the answer to one decimal place.

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### Video Transcript

A swimming pool is in the shape of a trapezoid. Find the length of one of the equal sides, giving the answer to one decimal place.

The length π΄π΅ is 15 metres. The length πΆπ· is nine metres. And the angles π΄π΅πΆ and π΅π΄π· are both 70 degrees. This means that length π΄π· and length πΆπ΅ are equal.

One way to solve this problem is to create a right-angled triangle. The length from π΅ to πΈ in this triangle is three metres. This is calculated by subtracting nine from 15 and dividing by two.

This problem can be solved using one of the trigonometrical ratios. Cos π is equal to the adjacent divided by the hypotenuse. The length π΅πΆ is the hypotenuse, as it is the longest side of the triangle and itβs opposite the right angle. The length π΅πΈ, three metres, is the adjacent, as it is adjacent or next to the 90-degree and 70-degree angles. Substituting these values into the formula gives us cos 70 is equal to three divided by π₯.

Rearranging this formula gives us π₯ is equal to three divided by cos 70. Typing this into our calculator gives us a value of π₯ of 8.8 to one decimal place. This means that the equal sides of the swimming pool, π΅πΆ and π΄π·, are equal to 8.8 metres.