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.
Well, well, well, looks like we have a trigonometry wizard here! Let's tackle this problem together, shall we?
You're on the right track with the tangent of 45 degrees. However, you made a small mistake when multiplying it by 20. You see, tan(45 degrees) is actually equal to 1, not 1.61.
So, let's try again. We have tan(45 degrees) = opposite/adjacent = 20/r. Since tan(45 degrees) = 1, we can rewrite the equation as 1 = 20/r.
To solve for r, we simply need to cross-multiply: r = 20.
There you have it! The hypotenuse, r, is equal to 20. Keep practicing those trig skills, my friend!
To solve for the length of the hypotenuse (r), you can use the trigonometric functions sine (sin) and cosine (cos).
In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, we are given the length of the opposite side as 20 and the angle as 45 degrees.
The equation for sine is sin(angle) = opposite/hypotenuse. Plugging in the values, we have:
sin(45 degrees) = 20/r.
We can rearrange this equation to solve for r:
r = 20/sin(45 degrees).
Now, let's calculate the value of r:
First, we need to find the sine of 45 degrees. The sine of 45 degrees is √2/2 (approximately 0.7071).
Substituting the value of sin(45 degrees) into the equation:
r = 20/0.7071.
Now, divide 20 by 0.7071 to find the value of r:
r ≈ 28.28.
Therefore, the length of the hypotenuse (r) is approximately 28.28.
To solve for the value of r, we can use the definition of tangent.
The tangent of an angle in a right triangle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this case, we know that the angle is 45 degrees and the opposite side is 20.
Using the tangent function, we have:
tan(45) = 20 / r
Since tan(45) is equal to 1, we can simplify the equation to:
1 = 20 / r
Now, to solve for r, we can cross-multiply:
r = 20 / 1
r = 20
So, the value of r in this right triangle is 20.