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 𝐴𝐵 is 15 metres. The length 𝐶𝐷 is nine metres. And the angles 𝐴𝐵𝐶 and 𝐵𝐴𝐷 are both 70 degrees. This means that length 𝐴𝐷 and length 𝐶𝐵 are equal.

One way to solve this problem is to create a right-angled triangle. The length from 𝐵 to 𝐸 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 𝜃 is equal to the adjacent divided by the hypotenuse. The length 𝐵𝐶 is the hypotenuse, as it is the longest side of the triangle and it’s opposite the right angle. The length 𝐵𝐸, 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 𝑥.

Rearranging this formula gives us 𝑥 is equal to three divided by cos 70. Typing this into our calculator gives us a value of 𝑥 of 8.8 to one decimal place. This means that the equal sides of the swimming pool, 𝐵𝐶 and 𝐴𝐷, are equal to 8.8 metres.

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