Question

How do you find the angle measure of the missing angle for a right triangle with one angle measure 0f “56” degree?

Answer 1

Hint: For finding the angle of a given triangle you need to have the measurement of the sides, which can be calculated by the given angles or of given in the question already. For finding the sides you have to use the trigonometry identity to find the values as we already know the trigonometry values for a given angle.
Formulae Used: \[\angle CAB + \angle ABC + \angle BCA = 180\](for any triangle)

Complete step-by-step answer:
The given triangle can be drawn as :
The assumed angle “x” needs to be obtained as per the given question, and two angle of triangle that are “90 and 56” are already given in the question.
Here we will use the summation of all interior angles of the triangle rule, which states that the sum of all interior angles of the triangle is “180 degree”.
Now using this formula we get:
\[
   \Rightarrow \angle CAB + \angle ABC + \angle BCA = 180 \\
   \Rightarrow 56 + x + 90 = 180 \\
   \Rightarrow x + 146 = 180 \\
   \Rightarrow x = 180 - 146 \\
   \Rightarrow x = 34\,\deg ree \;
 \]
The required angle asked in the question is “34”.
Formulae Used: \[\angle CAB + \angle ABC + \angle BCA = 180\](for any triangle)
So, the correct answer is “$ x = 34 \; Degree $”.

Note: Here we are to use the “sin” values to find the measurement of the sides but you can use any other trigonometric identity according to your ease. The only result we want is the measurement of the sides; it is up to us how we are going to find it and which identity suits best according to the data given in the question.