Question
Angle θ is an acute angle of a right triangle. Determine the value of cot θ given the value of sin θ below. what is sin 15/17?
Answers
GPT 3.5
To determine the value of cot θ, we need to find the value of cos θ.
Since θ is an acute angle of a right triangle, we can use the Pythagorean theorem to find the value of cos θ.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, let the length of the side opposite θ be 15 and the length of the hypotenuse be 17.
Using the Pythagorean theorem, we can find the length of the adjacent side:
17^2 = 15^2 + Adjacent Side^2
289 = 225 + Adjacent Side^2
Adjacent Side^2 = 289 - 225 = 64
Adjacent Side = √64 = 8
Now, we can find the value of cos θ by dividing the length of the adjacent side by the length of the hypotenuse:
cos θ = Adjacent Side / Hypotenuse = 8 / 17
Finally, we can find the value of cot θ by taking the reciprocal of the value of tan θ, which is equal to sin θ / cos θ:
cot θ = cos θ / sin θ = 8 / 15.
Hence, cot θ = 8/15.
Since θ is an acute angle of a right triangle, we can use the Pythagorean theorem to find the value of cos θ.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, let the length of the side opposite θ be 15 and the length of the hypotenuse be 17.
Using the Pythagorean theorem, we can find the length of the adjacent side:
17^2 = 15^2 + Adjacent Side^2
289 = 225 + Adjacent Side^2
Adjacent Side^2 = 289 - 225 = 64
Adjacent Side = √64 = 8
Now, we can find the value of cos θ by dividing the length of the adjacent side by the length of the hypotenuse:
cos θ = Adjacent Side / Hypotenuse = 8 / 17
Finally, we can find the value of cot θ by taking the reciprocal of the value of tan θ, which is equal to sin θ / cos θ:
cot θ = cos θ / sin θ = 8 / 15.
Hence, cot θ = 8/15.