Question

What is sin(c)? Explain your answer. b) What is tan(e)? Explain. c) What is mCE? Explain your answer.

A) a) Sin(c) is the sine of angle C, representing the ratio of the side opposite to C to the hypotenuse in triangle CDE.
B) b) Tan(e) is the tangent of angle E, representing the ratio of the side opposite to E to the side adjacent to E in triangle CDE.
C) c) mCE is the measure of angle CED, which can be found using the Law of Sines.

Answer 1

Sin(c) and Tan(e) refer to the trigonometric functions sine and tangent of angles C and E within a triangle, respectively. mCE refers to the measure of angle CED which can be found through trigonometric laws for non-right-angled triangles.

Step-by-step explanation:

Sin(c) is the sine of angle C, which, in a right-angled triangle, represents the ratio of the length of the side opposite to angle C to the length of the hypotenuse. For a right triangle with sides x (adjacent), y (opposite), and h (hypotenuse), sin(c) is calculated as y/h.

Tan(e) is the tangent of angle E, which also pertains to a right-angled triangle and represents the ratio of the length of the side opposite to angle E (y) to the length of the side adjacent to it (x), so tan(e) = y/x.

As for mCE or the measure of angle CED, it can be calculated if the triangle is not right-angled using trigonometric rules such as the Law of Sines or the Law of Cosines, depending on the known values. However, the Law of Sines relates the lengths of sides to the sines of their respective angles and is usually used for triangles that are not right-angled, thus it's not the best choice when you have a right-angled triangle.