For a given right triangle, side A = 490 ft and side b = 960 ft. What is the measure of angle B to the nearest degree?

assuming neither of the two given sides is the hypotenuse, make a sketch to see that

tan B = 960/490
angle B = appr 63°

To find the measure of angle B in a right triangle, you can use one of the trigonometric ratios, specifically the sine ratio.

The sine ratio is defined as the ratio of the length of the side opposite angle B (which is side A) to the length of the hypotenuse (the longest side, which is side c in this case).

In this problem, we are given the lengths of sides A and B, so we can use the sine ratio as follows:

sin(B) = A / c

First, we need to find the length of side c. In a right triangle, side c is the hypotenuse and is always the longest side. We can find its length using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides:

c^2 = A^2 + B^2

In this case:

c^2 = 490^2 + 960^2

Now we can solve for c by taking the square root of both sides:

c = sqrt(490^2 + 960^2)

Once we have the value of c, we can substitute it into the sine ratio equation to find the measure of angle B:

sin(B) = A / c

sin(B) = 490 / (sqrt(490^2 + 960^2))

Now, we can use the inverse sine function (sin^(-1)) to find the measure of angle B:

B = sin^(-1)(490 / (sqrt(490^2 + 960^2)))

Calculating the expression gives us:

B ≈ 29 degrees (to the nearest degree).

Therefore, the measure of angle B is approximately 29 degrees.