use trigonometric ratios and the Pythagorean theorem to solve the triangle.
h ttps://upload.wikimedia.org/wikipedia/commons/6/6f/Rtriangle.svg
c = 31.0 cm
a = 13.6 cm
we can find b using Pythagoras
a^2 + b^2 = c^2
13.6^2 + b^2 = 31^2
solve for b
sinA = 13.6/31 = .438709...
angle A = appr 26°
then angle B = 90-26 or 64°
of course angle C = 90°
thanks reiny
To solve the triangle, we can use trigonometric ratios and the Pythagorean theorem. Let's label the sides as shown in the image provided.
Side c is the hypotenuse, side a is the opposite side to angle A, and side b is the adjacent side to angle A.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Given c = 31.0 cm and a = 13.6 cm, we can substitute these values into the equation:
(31.0 cm)^2 = (13.6 cm)^2 + b^2
Now, let's solve for b:
b^2 = (31.0 cm)^2 - (13.6 cm)^2
b^2 = 961 - 184.96
b^2 = 776.04
Taking the square root of both sides:
b = sqrt(776.04) ≈ 27.87 cm
Now, let's calculate the trigonometric ratios for angle A:
Sin(A) = opposite/hypotenuse = a/c = 13.6/31.0 ≈ 0.439
Cos(A) = adjacent/hypotenuse = b/c = 27.87/31.0 ≈ 0.898
Tan(A) = opposite/adjacent = a/b = 13.6/27.87 ≈ 0.488
Therefore, we have found that side b is approximately 27.87 cm, and the trigonometric ratios for angle A are:
Sin(A) ≈ 0.439
Cos(A) ≈ 0.898
Tan(A) ≈ 0.488
Please note that the values are approximations and rounded for convenience.