Final answer:
To find the remaining ratios in the triangle with sides 5 and 4, we can use the Pythagorean theorem. We have sinθ = 5/√41, cosθ = 4/√41, and tanθ = 5/4.
Step-by-step explanation:
The given equation is 5² + 4² = c². To find the remaining ratios, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). So in this case, we have 5² + 4² = c². Evaluating the equation, we get 25 + 16 = c². Simplifying further, we get 41 = c². Taking the square root of both sides, we find c = √41.
Now, using the given ratio for tan (tanθ = a/b), we can find the remaining ratios. In a right triangle, the sine (sinθ) is defined as the ratio of the opposite side (a) to the hypotenuse (c), the cosine (cosθ) is defined as the ratio of the adjacent side (b), and the tangent (tanθ) is defined as the ratio of the opposite side (a) to the adjacent side (b).
So, in this case, we have tanθ = a/b = 5/4. To find sinθ and cosθ, we can use the properties of right triangles. Considering the triangle formed by the sides 5, 4, and c, we have sinθ = a/c = 5/√41 and cosθ = b/c = 4/√41.