Question
Kevin drew a triangle with angle measures of 30 degrees and 40 degrees and side measures of 5 cm, 7 cm, and 8 cm. Explain, using sides and angles, which type of triangle Kevin drew.
To determine the type of triangle Kevin drew, we can analyze the side measures and angle measures.
First, let's look at the side measures. The lengths of the sides are 5 cm, 7 cm, and 8 cm.
Using the side lengths, we can confirm that this is not an equilateral triangle because all three sides have different lengths.
Next, let's examine the angle measures. The given angle measures are 30 degrees and 40 degrees.
Since the sum of all interior angles of a triangle is always 180 degrees, we can calculate the measure of the third angle:
180 degrees - 30 degrees - 40 degrees = 110 degrees.
Now that we have the angle measures, we can determine the type of triangle based on them:
- If all three angles of a triangle are less than 90 degrees, it is classified as an acute triangle. In this case, 30 degrees, 40 degrees, and 110 degrees are all less than 90 degrees.
- If one angle of a triangle is exactly 90 degrees, it is called a right triangle. However, none of the angles in Kevin's triangle measure exactly 90 degrees.
- If one angle of a triangle is greater than 90 degrees, it is classified as an obtuse triangle. Again, none of the angles in Kevin's triangle are greater than 90 degrees.
Based on the side measures and angle measures, we can conclude that Kevin drew an acute triangle.