In right triangle ABC, ∠A is a right angle and sinC=15/17 What is the ratio cosC? Enter your answer as a fraction in simplest form, like this: 42/53

8/17

Step-by-step explanation:

Here, we should know that the sine of an angle is the ratio of the opposite to the hypotenuse

So in this case, 15 is the opposite and 17 is the hypotenuse

To find the cos of same angle, it is the ratio of the adjacent to the hypotenuse

We need the adjacent side

We can use Pythagoras’ theorem here

It states that the square of the hypotenuse equals sum of the squares of the two other sides

let’s say the adjacent is f

17^2 = 15^2 + f^2

f^2 = 17^2 -15^2

f^2 = 64

f = √(64)

f = 8

So the Cos C would be adjacent/hypotenuse = 8/17

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)