For a given right triangle, angle A = 61± and side b = 39 feet. What is the length of side a to the nearest foot?
To find the length of side 'a' in a right triangle with angle A equal to 61 degrees and side b equal to 39 feet, we can use the trigonometric function known as the sine ratio.
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to that angle (in this case, side 'a') divided by the length of the hypotenuse.
Since we know the length of side b and we are looking for the length of side a, we can use the sine function, which is given by the equation:
sin(A) = opposite/hypotenuse
Rearranging this equation, we get:
opposite = hypotenuse * sin(A)
Now, let's substitute the given values:
opposite = 39 * sin(61)
Using a scientific calculator or any calculator capable of calculating trigonometric functions, plug in the value of sin(61) and multiply it by 39:
opposite ≈ 39 * 0.8746 ≈ 34.07
Therefore, the length of side 'a' is approximately 34.07 feet when rounded to the nearest foot.