a. The order of the angle measures from least to greatest is:
m∠I < m∠HJI < m∠H
b. The order of the side lengths from least to greatest is:
JK < KL < JL
The figure you sent me appears to be a right triangle with a 90-degree angle at H. The side lengths of the triangle are given as 5 inches for HI and 12 inches for the hypotenuse JL. The two acute angles at the triangle are labeled as 52 degrees and 58 degrees.
a. The measures of the three angles from least to greatest. Based on the information given, we can see that:
m∠HJI is the right angle, so its measure is 90 degrees.
m∠I is the smaller of the two acute angles, with a measure of 52 degrees.
m∠H is the larger of the two acute angles, with a measure of 58 degrees.
Therefore, the order of the angle measures from least to greatest is:
m∠I < m∠HJI < m∠H
b. The side lengths JK, KL, and JL from least to greatest. In a right triangle, the hypotenuse is always the longest side. Therefore, we know that JL is the greatest side length.
To determine the order of JK and KL, we can use the sine function. The sine of an angle is equal to the opposite side divided by the hypotenuse. Since we have the measure of angle I (52 degrees) and the length of the hypotenuse (JL = 12 inches), we can calculate the length of JK using the following formula:
sin(52°) = JK / JL
Solving for JK, we get:
JK = JL * sin(52°) = 12 inches * sin(52°) ≈ 7.8 inches
Similarly, we can calculate the length of KL using the sine of angle H (58 degrees):
KL = JL * sin(58°) = 12 inches * sin(58°) ≈ 9.9 inches
Therefore, the order of the side lengths from least to greatest is:
JK < KL < JL