Video Transcript
Find the measure of the angles in a triangle given their ratio is four to five to nine. Give the answers to the nearest degree.
We recall that the angles in a triangle sum to 180 degrees. With any ratio question of this type, we begin by adding the ratios. We need to add four, five, and nine. This is equal to 18. Therefore, we have 18 parts in total. We need to divide 180 degrees by 18 to calculate the value of one part. 180 divided by 18 is equal to 10. This means that one part of the ratio is equal to 10 degrees. The ratio of the angles was four to five to nine. We need to multiply each of these by 10 degrees.
Four multiplied by 10 is equal to 40, five multiplied by 10 is 50, and nine multiplied by 10 is 90. The ratio four to five to nine is equivalent to the ratio 40 to 50 to 90. The measure of the three angles in the triangle are 40 degrees, 50 degrees, and 90 degrees. As one of them is equal to 90 degrees, we know this is a right-angled or right triangle. Whilst we were asked to give our answers to the nearest degree, we don’t need to round in this case as our answers are already whole numbers or integer values.
