Given b=48, A=36 degrees find the remaining parts of the right triangle.
B=
a)144 degrees
b)154 degrees
c)54 degrees
d)64 degrees
We know that one angle equals 36 and since it is a right triangle another must equal 90. The sum of the angles of a triangle is 180 meaning that we add 36 and 90 to get 126 and then subtract 126 from 180 leaving us with 54.
Did I do this the correct way it seems to easy?
yes correct
84
Looks like you made a little math error there. Since one angle is 36 degrees and another is 90 degrees, we need to find the measure of the third angle. The sum of the angles in a triangle is always 180 degrees. So, subtracting 36 and 90 from 180, we get 54 degrees for the remaining angle. The correct answer is C) 54 degrees. Keep up the good work, mathemagician!
To find the remaining parts of the right triangle, we can use the following trigonometric ratios:
1. Finding side B:
Using the sine ratio, sin(B) = b/h, where b is the side opposite angle B and h is the hypotenuse.
Substituting the given values, sin(B) = 48/h.
We need to find the value of h to determine angle B.
To find h, we can use the Pythagorean theorem.
Using a^2 + b^2 = c^2, where a and b are the legs of the right triangle and c is the hypotenuse.
Substituting the given values, a^2 + 48^2 = h^2.
36^2 + 48^2 = h^2.
Simplifying the equation, h^2 = 1296 + 2304 = 3600.
Taking the square root of both sides, h = √3600 = 60 (since h cannot be negative).
Now we can substitute the values into the sine ratio:
sin(B) = 48/60.
Calculating sin(B), sin(B) = 0.8.
Therefore, angle B = sin^(-1)(0.8) ≈ 53.13 degrees.
Thus, the remaining parts of the right triangle are:
B ≈ 53.13 degrees
To find angle B in the right triangle, you can start by using the fact that the sum of all angles in any triangle is equal to 180 degrees. In this case, we know that one angle is 36 degrees and another angle is 90 degrees since it is a right triangle.
So, the sum of the angles in this right triangle is 36 + 90 = 126 degrees. To find angle B, we subtract this value from 180 degrees since the sum of all angles in any triangle is 180 degrees.
180 - 126 = 54 degrees
Therefore, angle B is 54 degrees, so the correct answer is (c) 54 degrees.