In a certain right triangle, the two sides that are perpendicular to each other are 7.00 m and 8.30 m long. What is the tangent of the angle for which 7.00 m is the opposite side?
X = 8.30 m.
Y = 7.00 m.
Tan A = Y/X = 7.00/8.30 = 0.84337
Bobpursly, this is in my my physics book at the start of the section about vectors. I'd say that's physics.
Bob u r no help Iām sorry
Very helpful since I didn't know what tangent was. Never taken Trig.
To find the tangent of an angle, we need to use the trigonometric function "tangent", which is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, we have a right triangle with one side that is perpendicular to the angle we are interested in. The side 7.00 m is the opposite side to the angle we want to find the tangent of.
To find the tangent, we need to determine the length of the side adjacent to the angle. In a right triangle, the hypotenuse is always the longest side, and it is opposite the right angle. Thus, the hypotenuse is not relevant to finding the tangent of the angle in question.
Let's label the side adjacent to the angle as "x". By using the Pythagorean theorem, we can find the length of "x".
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:
x^2 = hypotenuse^2 - opposite side^2
Since the hypotenuse is not given, we will use the given side lengths to calculate the length of "x".
Plugging in the numbers, we have:
x^2 = (8.30 m)^2 - (7.00 m)^2
x^2 = 68.89 m^2 - 49.00 m^2
x^2 = 19.89 m^2
Taking the square root of both sides, we have:
x = ā19.89 m
Now that we have the length of the side adjacent to the angle, we can find the tangent of the angle. The tangent is defined as the ratio of the opposite side to the adjacent side.
Therefore, tangent of the angle = opposite side / adjacent side
tangent of the angle = 7.00 m / ā19.89 m
To calculate the numerical value, we can divide 7.00 m by the square root of 19.89 m using a calculator.
The tangent of the angle can be found by calculating 7.00 divided by the square root of 19.89, which is approximately 0.84.
Therefore, the tangent of the angle for which 7.00 m is the opposite side is approximately 0.84.