In a triangle, GHI, if sin G = 8/17 then what is the value of cos H?
A). 8/17
B). 15/8
C). 15/17***
D). 17/8
Nope. 15/17 = cosG
cosH = sinG
Draw the triangle to see this.
The "co" in cosine means sine of the complementary angle.
looking at the numbers showing up , I can see that
15^2 + 8^2 = 17^2
thus suggesting that you have a right-angled triangle.
You did not state that all important information.
Assuming that angles G and H are the acute angles of such a triangle
we know that sin G = cos(90°- G) = cos H , since G and H must be complimentary angles
so cos H = 8/17
@oobleck I assumed since the denominator was 17, that meant that the answer should have the same amount as what was in the question
@Spring, please be polite here, whether to tutors or other students.
To indicate a website, all you have to do is omit the https:// part, and the rest will paste just fine. All tutors know this. Be sure you give it a try.
Spring, you are correct. So?
To find the value of cos H in triangle GHI, where sin G = 8/17, we can use the Pythagorean identity in trigonometry.
The Pythagorean identity is given by:
sin^2(x) + cos^2(x) = 1
Let's substitute sin G into the equation:
(8/17)^2 + cos^2(H) = 1
Simplifying this equation, we have:
64/289 + cos^2(H) = 1
Now, subtracting 64/289 from both sides of the equation, we get:
cos^2(H) = 1 - 64/289
Next, we can take the square root of both sides to solve for cos H:
cos(H) = √(1 - 64/289)
Now, calculating the value inside the square root:
cos(H) = √(289/289 - 64/289)
cos(H) = √(225/289)
Simplifying the square root:
cos(H) = 15/17
Therefore, the value of cos H is 15/17.
So, the correct option is C) 15/17.