Question Video: Using Right Triangle Trigonometry to Find an Unknown Length Mathematics

Video Transcript

Find 𝑥 to two decimal places.

In order to solve this problem, we are going to have to use the sine, cosine, and tangent trigonometrical ratios. sin 𝜃 is equal to the opposite divided by the hypotenuse, cos 𝜃 is equal to the adjacent divided by the hypotenuse, and tan 𝜃 is equal to the opposite divided by the adjacent.

We will start this question by labelling the sides on the right-angled triangle. The hypotenuse is the longest side or the side that is opposite the right angle — in this case 10. The side labelled 𝑥 is the opposite as it is opposite the 55-degree angle. And the third side is the adjacent as it is next to the 55-degree and 90-degree angles.

As the 𝑥 and the 10 are on the opposite and the hypotenuse, we’re going to use the sine ratio. Substituting in our values gives us an equation: sin 55 equals 𝑥 divided by 10. Multiplying both sides of the equation by 10 gives us 10 multiplied by sin 55 equals 𝑥.

Typing this into our calculator gives us a value for 𝑥 of 8.19 to two decimal places.