Suppose <A is one of the acute angles formed by the line x+2y=6 and the x axis. What is the approximate measure of <A to the nearest degree of <A?
1. x + 2y = 6.
Slope = -a/b = -1/2 = -0.50.
tanA = -0.50.
A = 27o.
triangle abc has sides a=11 b=13 and c=15. find the sum of the angles supplementary to angles a, b, c
To find the measure of angle A, you need to determine the coordinates of the point where the line x+2y=6 intersects the x-axis. Once you have the coordinates of this point, you can use trigonometry to find the measure of angle A.
First, let's find the coordinates of the point where the line intersects the x-axis:
Set y to 0 in the equation x+2y=6:
x + 2(0) = 6
x = 6
Therefore, the point where the line intersects the x-axis is (6, 0).
Now, we have two points: (6, 0) and the origin (0, 0). These two points form a right-angled triangle along with the point (6, 0). Angle A is one of the acute angles of this triangle.
To find the measure of angle A, we can use the tangent function. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle.
In our case, the opposite side is the length of the y-coordinate of the point (6, 0), which is 0, and the adjacent side is the length of the x-coordinate, which is 6.
Using the formula for tangent:
tan(A) = opposite / adjacent
tan(A) = 0 / 6
tan(A) = 0
Taking the arctan of both sides:
A = arctan(0)
Now, if you calculate the arctan(0) using a calculator or by referencing a trigonometric table, you will find that the value is 0 degrees.
Therefore, the approximate measure of angle A to the nearest degree is 0 degrees.