In right triangle ABC, ∠A is a right angle and sinC=1517.
Triangle A B C with a right angle at A and hypotenuse B C.
What is the ratio cos C?
Enter your answer as a fraction in simplest form, like this: 42/53
To find the ratio of cos C, we can use the Pythagorean identity which states that cos^2 C + sin^2 C = 1. Since sin C is given as 1517, we can substitute it into the equation.
cos^2 C + (1517)^2 = 1
Now, we can solve for cos C.
cos^2 C = 1 - (1517)^2
cos C = √(1 - (1517)^2)
Simplifying, we have:
cos C = √(1 - 1517^2)
Therefore, the ratio of cos C is:
cos C = √(1 - 1517^2)
Please note that the exact value of cos C cannot be determined without knowing the other angles in the triangle.
To find the ratio cos C, we first need to find the value of cos C.
Since sin C = opposite/hypotenuse, we know that sin C = BC / AB. We also know that cos C = adjacent/hypotenuse.
To find the value of cos C, we need to find the value of the adjacent side (AC).
Since AC and BC are two sides of a right triangle, we can use the Pythagorean theorem:
AC^2 + BC^2 = AB^2
We already know the value of sin C, which is BC / AB. We can substitute this information into the Pythagorean theorem:
AC^2 + (sin C * AB)^2 = AB^2
Now we can solve for AC:
AC^2 + (1517 * AB)^2 = AB^2
AC^2 + 1517^2 * AB^2 = AB^2
AC^2 = AB^2 - 1517^2 * AB^2
AC^2 = AB^2 * (1 - 1517^2)
AC = √(AB^2 * (1 - 1517^2))
Now that we have AC, we can find cos C:
cos C = adjacent / hypotenuse
cos C = AC / AB
Substituting the value of AC, we have:
cos C = √(AB^2 * (1 - 1517^2)) / AB
The ratio cos C is therefore the square root of (AB^2 * (1 - 1517^2)) over AB.
Now we need to simplify the expression. Unfortunately, we don't have the lengths of any sides of the triangle, so we cannot calculate the exact value of cos C or simplify the expression any further.
Therefore, the answer is: cos C = √(AB^2 * (1 - 1517^2)) / AB