Mathematics

Question

I need help! This is Geometry lesson 8-3 ! Please help me asap!!!!
I need help! This is Geometry lesson 8-3 ! Please help me asap!!!!

1 Answer

  • If you learned about the 45-45-90 triangle (which is isosceles), then the faster way is to know that the hypotenuse (side opposite of right angle) is √2 times either one of the sides.
    3√2 = (√2)x
    x = 3

    But if you didn't learn the 45-45-90 triangle yet, that's ok.
    Recall the trigonometric ratios for right triangles: sine (sin), cosine (cos), tangent (tan).

    If your angle is x, then
    sin(x) = opposite side / hypotenuse
    cos(x) = adjacent side / hypotenuse
    tan(x) = opposite side / adjacent side

    Remember the hypotenuse is the side opposite and across from the right angle (3√2 in this case).
    An acronym to remember this is SohCahToa.

    In this problem, the angle given is 45°, and you need to find the length of the adjacent side x. The hypotenuse is also given as 3√2.

    Because we have the adjacent side and the hypotenuse, we use cosine to relate those two sides
    cos(45°) = x / (3√2)
    x = (3√2)cos45°
    If you plug this into your calculator (in degree mode), then
    x = 3

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