I'm learning about trigonometric functions, and my worksheet instructs me to find the "missing information" for each triangle.
For the first one, they give me the length of the hypotenuse (45) and that theta = 35. How can I go about finding the missing info?
sin35=Opposite/45 do this to find the opposite
if it is a right triangle use a^2+b^2=c^2 to find the other side
take 35+90-180 to find the other angle
ONLY IF A RIGHT TRIANGLE
Ok cool, I got that. Thanks a lot.
However, this next one gives me the length of one leg (359) and the adjacent theta of 83. How exactly can I solve this?
To solve for the missing information in a right triangle, you can use the trigonometric functions: sine (sin), cosine (cos), and tangent (tan).
In this case, you are given the length of the hypotenuse (45) and the measure of one of the angles (θ = 35°). To find the missing information, you can use the sine, cosine, or tangent function, depending on what you are trying to solve for.
To find the length of the side adjacent to the angle (let's call it "x"), you can use the cosine function: cos(θ) = adjacent/hypotenuse. In this case, cos(35°) = x/45. Solving for x, you can multiply both sides by 45 and find that x ≈ 36.37.
To find the length of the side opposite to the angle (let's call it "y"), you can use the sine function: sin(θ) = opposite/hypotenuse. In this case, sin(35°) = y/45. Solving for y, you can multiply both sides by 45 and find that y ≈ 25.79.
To find the value of the hypotenuse, you can use either the sine or the cosine function, depending on what information you have. Since you already have the hypotenuse (45), you don't need to find it again.
In summary:
- To find the length of the side adjacent to the angle (x): x ≈ 36.37
- To find the length of the side opposite to the angle (y): y ≈ 25.79
- The length of the hypotenuse is given as 45.