Solving an Angle with Trigonometry

[klm]

edit- nevermind i got it
okay what i figured so far is that the angle i am looking for is 30 degrees, b/c that bottom angle is 45, so the other angle total should be 45. and then i subtracted 15 and got 30. so i am thinking that the component that is suppose to be tangent would be 2cos30=Ay ...would that be correct?
and i have no idea how i am suppose to get the perpendicular one. any help would be greatly appreciated!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[klm]

so really the tangent would be 2sin30 ?

 

[m2003]

Trigonometry is a powerful tool for solving angles and other geometric problems. In this case, it appears that you are trying to find the value of an unknown angle in a triangle. It is important to remember that in a triangle, the sum of all three angles is always 180 degrees. So, if one angle is known to be 45 degrees, then the other two angles must add up to 135 degrees.

To find the value of the unknown angle, you correctly subtracted 15 degrees from the total of 45 degrees and got 30 degrees. This is a valid approach, but there is another way to solve this problem using trigonometric ratios.

In a right triangle, the tangent of an angle is equal to the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, the angle you are trying to find is the one opposite the side with a length of 2, and the adjacent side has a length of Ay. So, using the tangent ratio, we can set up the following equation:

tan 30 = 2/Ay

Solving for Ay, we get Ay = 2/tan 30. Using a calculator, we can find that the value of tan 30 is approximately 0.5774. So, Ay = 2/0.5774 = 3.4641.

To find the perpendicular component, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we know that the hypotenuse has a length of 5, and one of the sides has a length of 2. So, using the Pythagorean theorem, we can set up the following equation:

5^2 = 2^2 + Ay^2

Solving for Ay, we get Ay = √(5^2 - 2^2) = √21 ≈ 4.5826.

So, the two components we were looking for are Ay = 3.4641 and the perpendicular component ≈ 4.5826. I hope this helps!