If c=17 in. and b=15 in. , find the value of sinθ . Write your answer as a fraction. You do not need to simplify.
To find the value of sinθ, we can use the Pythagorean theorem, which states that for any 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).
In this case, we have c = 17in and b = 15in. Let a represent the length of the remaining side.
Using the Pythagorean theorem:
a^2 + b^2 = c^2
a^2 + (15in)^2 = (17in)^2
a^2 + 225in^2 = 289in^2
a^2 = 289in^2 - 225in^2
a^2 = 64in^2
Taking the square root of both sides:
a = √(64in^2)
a = 8in
Now we can find the value of sinθ by dividing the length of the side opposite the angle (a) by the length of the hypotenuse (c):
sinθ = a/c
sinθ = 8in / 17in
sinθ = 8/17