what are the angle measures of the triangle? the image shows a right triangle. the bottom side is 21, the side is 7√3 and the hypotenuse is 14√3

Answer 1

To find the angle measures of the right triangle, we can use the trigonometric functions.

The given values are the sides of the right triangle: the bottom side is 21, the side is 7√3, and the hypotenuse is 14√3.

To find the angle opposite the side with length 7√3:

sin(angle) = (opposite side/hypotenuse)
sin(angle) = (7√3)/(14√3)
sin(angle) = 1/2

From the unit circle, we find that the angle whose sine is 1/2 is 30 degrees. Therefore, the angle opposite the side with length 7√3 is 30 degrees.

To find the angle opposite the side with length 21:

cos(angle) = (adjacent side/hypotenuse)
cos(angle) = 21/(14√3)
cos(angle) = √3/2

From the unit circle, we find that the angle whose cosine is √3/2 is 30 degrees. Therefore, the angle opposite the side with length 21 is also 30 degrees.

Lastly, to find the right angle, it is always 90 degrees.

Therefore, the angle measures of the triangle are:

Angle opposite side with length 7√3 = 30 degrees
Angle opposite side with length 21 = 30 degrees
Right angle = 90 degrees