Question

The number of degrees in an acute angle of a right – angled triangle is equal to the number of grades in the other; express both the angles in degrees.

Answer 1

Hint:-Before solving this question, we must know about the conversion of Degree and Grades.
So, if we have ‘D’ degree and ‘G’ grades, then:-
$\dfrac{D}{90}=\dfrac{G}{100}$
Complete step-by-step answer:
So, we will be using this formula for the solution of this question, i.e. for solving this question.
Let us now solve this question.
Let one acute angle (in degrees) be ‘x’ degrees.
As we know that the sum of all the angles of any triangle is 180 degrees, therefore:-
90 + x + third angle = 180 degree
Therefore, the measure of the third angle = ‘90 –x’ degrees.
We know that $\dfrac{D}{90}=\dfrac{G}{100}$
Therefore, $\dfrac{90-x}{90}=\dfrac{G}{100}$
Hence, we get:-
9G = 10 (90 –x)
9G = 900 – 10x
G = $\dfrac{900-10x}{9}$
Now, according to the question,
$\dfrac{900-10x}{9}=\dfrac{x}{1}$
9x = 900 – 10x
19x = 900 $~=\text{ }\dfrac{900}{19}\text{ }=\text{ }47.37{}^\circ$
So, as the third angle = 90° –x, therefore, its measure is:-
90° - 47.37° = 42.63°
Hence, we get our answers.
The measures of the two acute angles are 42.63° and 47.37°.

Note:-The students must know about the conversion of Degree to Grades that we use for the conversion of degrees to grades.
If we have ‘D’ degree and ‘G’ grades, then:-
$\dfrac{D}{90}=\dfrac{G}{100}$
If the students do not know about these conversion methods, then he/she will not be able to solve such questions.
Also, one must be very careful while doing the calculus part of such questions, as any mistake or error can make the answer wrong.