solve for r
There is a right triangle with the hypotenuse as r , the angle as 45 degrees and opposite side as 20.
I am having a hard time finding this out. I had tan 45 = 1.61 20(1.61) = 32.4 but this is wrong.
A basic rule for right triangles is sine(theta) = opposite/hypotenuse
20 = your opposite side
theta is your angle
rearrange to fit your problem:
hypotenuse = opposite/sin(theta)
plug in and solve
make sure your calculator is in degrees, not radians too.
what you did wrong was this:
tan(theta) = opposite / adjacent
An easy trick to remember is SOHCAHTOA (pronounced so-ka-toe-a):
sin (S) is opposite(O)/hypotenuse(H)
cos (C) is adjacent (A)/hypotenuse(H)
tan (T) is opposite (O)/adjacent (A)
I'm in college calculus now, and I still use that trick to remember.
To solve for the value of r in the given right triangle, you can use the sine function. Given that the opposite side is 20 and the angle is 45 degrees, we can write the equation as:
sin(45 degrees) = opposite / hypotenuse
Substituting the known values:
sin(45 degrees) = 20 / r
Now, to isolate r, we can rearrange the equation:
r * sin(45 degrees) = 20
To find the value of r, we need to evaluate the sin(45 degrees). The sine of 45 degrees is equal to 1 / √2, which is approximately 0.707.
Plugging in this value:
r * 0.707 = 20
Now, divide both sides of the equation by 0.707:
r = 20 / 0.707
Evaluating this expression:
r ≈ 28.28
Therefore, the value of r in the given right triangle is approximately 28.28.