The measure of angle E is 17.4 degrees.
The triangle in the image is a right triangle, which means we can use trigonometry to solve for the missing angle. We are given that the length of the hypotenuse is 17 and the length of one leg is 5.4. We need to solve for the measure of angle E, which is adjacent to the leg with length 5.4.
There are two ways to solve for angle E using trigonometry:
1. Using the tangent function (tan):
tan(E) = (leg adjacent to E) / (leg opposite to E)
tan(E) = 5.4 / (unknown)
Since we are solving for angle E, the leg opposite to E is the hypotenuse, which has a length of 17.
tan(E) = 5.4 / 17
E = arctan(5.4 / 17)
Using a calculator, we get E ≈ 17.4°
2. Using the sine function (sin):
sin(E) = (leg opposite to E) / (hypotenuse)
sin(E) = (unknown) / 17
Since we are solving for angle E, the leg opposite to E is the leg with length 5.4.
sin(E) = 5.4 / 17
E = arcsin(5.4 / 17)
Using a calculator, we get E ≈ 17.4°
Therefore, the measure of angle E is approximately 17.4 degrees.
Rounding to the nearest tenth of a degree:
17.4 degrees rounded to the nearest tenth is 17.4 degrees.
The measure of angle E is 17.4 degrees.