In right triangle ABC, the length of side is 12 , the measure of is , and is a right angle. Which of the following can be determined using the information given?
I) The measure of
II) The length of side

The correct answer is: I and II

As stated in the problem statement, is a right angle of right triangle ABC then, is the hypotenuse. Consider the following diagram,
Explanation:
Step 1 of 2:
Given, , and .

We know that the sum of all three angles of a triangle is .
Here,



The value of is .
Step 2 of 2:
We know that in a right triangle, , where is the angle between hypotenuse and height of the triangle.
Thus, in the given ,

The measure of is .
Final Answer:
The right option is — I and II.

Any triangle that has one 90-degree angle is said to have a right angle. Right triangles are those with an angle of 90 degrees, or "right angles," hence those with this angle. First, determine the third angle's measurement. You already know that C = 90 degrees because it is a right angle, and you are also aware of the size of A or B. Since a triangle's internal degree measurement must always equal 180 degrees, the third angle's measurement can be determined by applying the following formula: 180 – (90 + A) = B. The formula can also be turned around so that 180 - (90 + B) = A.
As an illustration, if you know that A is 40 degrees, then B is 180 – (90 – 40). It is easy to work out that B = 50 degrees if you simplify this to B = 180 - 130. Triangles can be resolved using the Law of Sines. Knowing the length of one side and the measurement of one other angle in addition to the right angle will especially assist you in finding the hypotenuse of a right triangle. The Law of Sines asserts that for any triangle with sides a, b, and c and angles a, b, and c, a / sin A = b / sin B = c / sin C.
Any triangle can be resolved using the Law of Sines, but only a right triangle will have a hypotenuse.