Hi! I am super confused with this question and really need help.
In a right triangle with a leg of 4 and a hypotenuse of 8, find the measures of all angles.
a. 27 degrees, 63 degrees, 90 degrees
b. 30 degrees, 60 degrees, 90 degrees
c. 40 degrees, 50 degrees, 90 degrees
d. 45 degrees, 45 degrees, 90 degrees
a = 4, b = ?, c = 8.
a^2 + b^2 = c^2.
4^2 + b^2 = 8^2,
b = 6.93.
Cos B = a/c = 4/8 = 0.50.
B = 60o.
A + B = 90o
A + 60 = 90,
A = 30o.
C = 90o.
So A = 30o, B = 60o, and C = 90o.
To find the measures of all angles in a right triangle with a leg of 4 and a hypotenuse of 8, we can use the trigonometric ratios sine, cosine, and tangent.
Let's start by labeling the triangle. Let one leg be the adjacent side (A), the other leg be the opposite side (O), and the hypotenuse be H. In this case, A = 4 and H = 8.
We can use the cosine ratio:
cos(theta) = A/H
cos(theta) = 4/8
cos(theta) = 1/2
Now, we need to find the angle whose cosine is 1/2. We can use the inverse cosine function or the cosine table to find the angle whose cosine is 1/2.
cos^-1(1/2) is approximately 60 degrees. Therefore, one of the angles in our right triangle is 60 degrees.
Since it is a right triangle, the sum of the other two angles must be 90 degrees. Thus, the remaining two angles are 30 degrees and 90 degrees.
Therefore, the correct answer is b. 30 degrees, 60 degrees, 90 degrees.