Answer
Verified
414.3k+ views
Hint: Draw a line perpendicular to the base line and assume the complementary angle to be $x$. Subtract the given angle from ${{90}^{\circ }}$ to find the value of $x$. The value of $x$ obtained will be the answer.
Complete step-by-step answer:
Complementary angles are angle pairs whose measures sum to one right angle or ${{90}^{\circ }}$. If two complementary angles are adjacent their non-shared side forms a right angle. In Euclidean geometry, the two acute angles in a right angle triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees. The adjective complementary is from Latin complementum, associated with the verb complete, “to fill up”. An acute angle is filled up by its complement to form a right angle. The difference between an angle and a right angle is termed as the complement of the angle.
If two A and B angles are complementary, the following relationships hold:
$\begin{align}
& {{\sin }^{2}}A+{{\sin }^{2}}B=1 \\
& \tan A=\cot B \\
& {{\cos }^{2}}A+{{\cos }^{2}}B=1 \\
& \sec A=\cos ecB \\
\end{align}$
The tangent of an angle equals the cotangent of its complement and its secant equals the cosecant of its complement. The prefix “co-“ in the names of some trigonometric ratios refers to the word “complementary”.
Now, we come to the question. Let us assume that the complementary angle of \[{{57}^{\circ }}\] is $x$. Then, $\begin{align}
& x+{{57}^{\circ }}={{90}^{\circ }} \\
& x={{90}^{\circ }}-{{57}^{\circ }} \\
& x={{33}^{\circ }} \\
\end{align}$
Hence, the complementary angle is ${{33}^{\circ }}$.
Note: We don’t have to equate the sum equal to ${{180}^{\circ }}$ because that will be the pair of supplementary angles. So, for finding the complementary angle we have to put the sum of all given angles equal to ${{90}^{\circ }}$.Complementary angles are angle pairs whose measures sum to one right angle or ${{90}^{\circ }}$.Supplementary angles are angle pairs whose measures sum to one straight angle or ${{180}^{\circ }}$.
Complete step-by-step answer:
Complementary angles are angle pairs whose measures sum to one right angle or ${{90}^{\circ }}$. If two complementary angles are adjacent their non-shared side forms a right angle. In Euclidean geometry, the two acute angles in a right angle triangle are complementary, because the sum of internal angles of a triangle is 180 degrees, and the right angle itself accounts for ninety degrees. The adjective complementary is from Latin complementum, associated with the verb complete, “to fill up”. An acute angle is filled up by its complement to form a right angle. The difference between an angle and a right angle is termed as the complement of the angle.
If two A and B angles are complementary, the following relationships hold:
$\begin{align}
& {{\sin }^{2}}A+{{\sin }^{2}}B=1 \\
& \tan A=\cot B \\
& {{\cos }^{2}}A+{{\cos }^{2}}B=1 \\
& \sec A=\cos ecB \\
\end{align}$
The tangent of an angle equals the cotangent of its complement and its secant equals the cosecant of its complement. The prefix “co-“ in the names of some trigonometric ratios refers to the word “complementary”.
Now, we come to the question. Let us assume that the complementary angle of \[{{57}^{\circ }}\] is $x$. Then, $\begin{align}
& x+{{57}^{\circ }}={{90}^{\circ }} \\
& x={{90}^{\circ }}-{{57}^{\circ }} \\
& x={{33}^{\circ }} \\
\end{align}$
Hence, the complementary angle is ${{33}^{\circ }}$.
Note: We don’t have to equate the sum equal to ${{180}^{\circ }}$ because that will be the pair of supplementary angles. So, for finding the complementary angle we have to put the sum of all given angles equal to ${{90}^{\circ }}$.Complementary angles are angle pairs whose measures sum to one right angle or ${{90}^{\circ }}$.Supplementary angles are angle pairs whose measures sum to one straight angle or ${{180}^{\circ }}$.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE