For a given right triangle, angle B = 46±

and side c = 30 feet. What is the length of side a to the nearest foot?

assuming A is the right angle,

cosB = 30/a
a = 30/cos46° = 43.19

For a given right triangle, angle A = 61± and side b = 39 feet. What is the length of side c to the nearest foot?

3467

To find the length of side "a" in a right triangle, we can use the sine function. The sine function relates the length of the side opposite an angle to the length of the hypotenuse.

In this case, we are given the angle B, which is 46±. Since angle B is acute in a right triangle, it means angle B is 46 degrees (assume the positive value).

Now, we can use the sine function: sin(B) = opp/hyp. Rearranging the formula, we have opp = sin(B) * hyp.

Using the given values, B = 46 degrees and hypotenuse c = 30 feet, we can calculate the length of side a:

sin(46°) ≈ 0.7193

opp = 0.7193 * 30
opp ≈ 21.579 feet

Therefore, the length of side a is approximately 21.579 feet, rounded to the nearest foot.