For the given figure, find 𝑥 to two decimal places.
As the triangle is right-angled, we can solve this problem using the trigonometrical ratios, also known as SOHCAHTOA. Our first step is to label the triangle to decide which of the ratios to use. The longest side of the triangle opposite the right angle is called the hypotenuse. The angle opposite the angle we’re going to use, in this case 55 degrees, is known as the opposite. And finally, the side next to the 55-degree angle and the right angle is known as the adjacent.
In this question, our adjacent is equal to 𝑥 and our hypotenuse is equal to 10. This means that we need to use the cosine ratio. Cos of 𝜃 is equal to the adjacent divided by the hypotenuse. Substituting in our values from the diagram gives us cos of 55 is equal to 𝑥 divided by 10. Multiplying both sides of this equation by 10 gives us 10 multiplied by cos of 55 is equal to 𝑥.
Ensuring our calculator is in degree mode, we can then type 10 multiplied by cos 55 into the calculator. This gives us an answer of 5.73576, and so on. We were asked to give our answer to two decimal places. This means that we want two numbers after the decimal point. The deciding number is the five that we have underlined. If this is five or bigger, we need to round up. This means that 𝑥 is equal to 5.74.
A good check at this point is to ensure that our value for our adjacent is less than the value for the hypotenuse, as the hypotenuse is the longest side of the triangle. 5.74 is less than 10, so our answer is sensible.