Find the ratio....................

Question

Answer 1

To find the ratio of tangent of "R", you'll need to find the opposite and adjacent sides to "R". You are given the adjacent side, but you'll need to find the opposite.

You can do this by using the Pythagorean theorem to find side ST (opposite of "R").

a² + b² = c²

(ST)² + (9)² = (14)²

(ST)² + 81 = 196 (then subtract 81 from both sides and take the square root)

ST = Square root (115)

ST = about 10.7

Therefore,

Tan (R) = 10.7/9 (which would be the ratio)

If asked to solve,

Tan^-1(10.7/9) = R = about 49.9 degrees

Answer 2

tanR = ST/RT= sqr(14^2-9^2)/9 = 10.72/9 =1.2

tan(R) = 1.2

Answer 3

This one's about both tangent and pythagorean's theorem. To use tangent, we need to know the lengths of the sides opposite and adjacent (adjacent means the side closest to the angle, but not the hypotenuse) to the angle (R).

To find the length of the side opposite from the angle, fill in the equation a² + b² = c² :

9² + b² = 14²

Rearranging this, we get b² = 14² - 9² (remember that 'b' here is the length of the side opposite from the angle.)

We need to solve for just 'b', not b². So to turn that b² into just 'b', I need to take the square root of both sides. This turns the equation into:

b = √(14² - 9²)

b = 10.7

Now that we know the opposite side's length (10.7), we can use that in our tangent equation.

Tangent of an angle is always equal to the length of the side opposite to it divided by the length of the side adjacent to it. In this case, tan(R) = 10.7 / 9

So your ratio is 10.7 / 9