Video: Finding the Unknown Angle in a Right Triangle Using Trigonometry

For the given figure, find the measure of angle πœƒ, in degrees, to two decimal places.


Video Transcript

For the given figure, find the measure of angle πœƒ in degrees to two decimal places.

As the triangle is right-angled, we can use the trigonometrical ratios sine, cosine, and tangent, shortened to sin, cos, and tan. In any right-angled triangle, sin πœƒ is equal to the opposite divided by the hypotenuse, cos πœƒ is equal to the adjacent side divided by the hypotenuse, and tan πœƒ is equal to the opposite divided by the adjacent.

Our first step is to label the triangle. The longest side of a right-angled triangle is the hypotenuse. The other two sides are determined by which angle we’re dealing with: which one is opposite the angle πœƒ and which side is adjacent to the angle πœƒ. Well, in this case, the side labelled three is adjacent to the angle πœƒ and the other side is opposite the angle.

As our measurements are on the adjacent and the hypotenuse, we’re going to use the ratio cos πœƒ equals the adjacent divided by the hypotenuse. Substituting the values into the formula gives us cos πœƒ equals three divided by eight or three-eighths.

In order to calculate the angle, we need to use the inverse function or cos to the minus one. Therefore, πœƒ equals inverse cos of three-eighths. Ensuring our calculator is in degree mode, we can type this in, giving us an answer πœƒ equals 67.98 degrees. This value has been rounded to two decimal places.

The trigonometrical ratios can be used to find missing angles or missing sides in right-angled triangles. Whenever we wish to find a missing angle, we will have to use the inverse function: inverse sin, inverse cos, or inverse tan.

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