Is this statement always, sometimes, or never true?If ∠T and ∠U are complementary angles and m∠U is more than 55°, then sin(T)=sin(U).
Question
Is this statement always, sometimes, or never true?If ∠T and ∠U are complementary angles and m∠U is more than 55°, then sin(T)=sin(U).
Solution
This statement is never true. Here's why:
-
Complementary angles are two angles whose measures add up to 90 degrees. So if ∠T and ∠U are complementary, then m∠T + m∠U = 90°.
-
The problem states that m∠U is more than 55°. This means that m∠T must be less than 35° (since 90 - 55 = 35).
-
The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse.
-
The sine function is not the same for all angles. Specifically, sin(T) does not equal sin(U) for all values of T and U.
-
Therefore, if m∠T is less than 35° and m∠U is more than 55°, then sin(T) cannot equal sin(U). So the statement is never true.
Similar Questions
Is this statement always, sometimes, or never true?If ∠T and ∠U are complementary angles, then cos(U)=sin(T).alwayssometimesneverSubmit
Is this statement always, sometimes, or never true?If m∠K is between 50° and 60°, then sin(K)=cos(K).alwayssometimesneverSubmit
Is this statement always, sometimes, or never true?For two acute angles ∠J and ∠K, if m∠J+m∠K=90°, then sin(J)=cos(K).alwayssometimesneverSubmit
Is this statement always, sometimes, or never true?If ∠H and ∠J are acute angles in a scalene right triangle, then sin(H)=sin(J).alwayssometimesneverSubmit
Is this statement always, sometimes, or never true?If ∠L is an angle in a right triangle and m∠L is between 30° and 50°, then sin(L)=cos(L).alwayssometimesneverSubmit
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.