Find 𝑥. Give your answer to two decimal places.
As the triangle is right angled, we can solve this problem using the trigonometrical ratios, sometimes known as SOHCAHTOA. Our first step is to label the sides of the triangle. The longest side of a right-angled triangle is known as the hypotenuse. The side opposite the 41-degree angle is the opposite. And finally the side next to the 41-degree angle and the 90-degree angle is the adjacent.
In this question, our 𝐻 is equal to 12 and our 𝐴 is equal to 𝑥. We’ll therefore use the trigonometrical ratio that has 𝐴 and 𝐻. This is cosine or cos. Cos of 𝜃 is equal to the adjacent divided by the hypotenuse. Substituting in the angle 41 degrees and our values of 𝐻 and 𝐴 gives us cos 41 is equal to 𝑥 divided by 12.
Multiplying both sides of this equation by 12 gives us 12 multiplied by cos of 41 is equal to 𝑥. Ensuring our calculator is in degree mode, 12 multiplied by cos of 41 is equal to 9.0565 and so on. We were asked to round our number to two decimal places. This means our answer must have two numbers after the decimal point. Our deciding number is the six. As this is greater than five, we will round up.
Rounding our answer up gives us a value of 𝑥 of 9.06. A good check at this point is to make sure that our value for our adjacent is less than the hypotenuse as the hypotenuse is the longest side of a right-angled triangle. 9.06 is less than 12. So our answer is sensible.