For a given right triangle, side a = 400 feet andside b = 900 feet.What is the measure of angle A to the nearest degree

tanA = 4/9

A = 24°

big doinks in amish

To find the measure of angle A in a right triangle, you can use the inverse tangent function (tan⁻¹) or the inverse sine function (sin⁻¹) depending on the given sides.

In this case, we know the lengths of sides a and b, so we can use the inverse tangent function.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle (a) to the length of the side adjacent to the angle (b). Therefore, we can use the tangent function to find the measure of angle A.

The formula for calculating the tangent of an angle is:
tan(θ) = opposite side / adjacent side

In this case, we have:
tan(A) = a / b

Substituting the given values into the formula, we get:
tan(A) = 400 / 900

Now, we can use the inverse tangent function (tan⁻¹) to find the angle A:
A = tan⁻¹(400 / 900)

Using a scientific calculator or trigonometric table, you can find the inverse tangent of 400 / 900. This gives us the value of angle A in radians.
To convert radians to degrees, you can use the conversion factor: 1 radian = 180/π degrees.

Multiply the value in radians by the conversion factor to get the measure of angle A in degrees. Lastly, round the answer to the nearest degree.

So, using this method, you can find the measure of angle A to the nearest degree in a right triangle.