For a given right triangle, side a = 490 feet and side b = 960 feet. What is the measure of angle B to the nearest degree?
To find the measure of angle B in a right triangle, we can use trigonometric functions. In this case, we can use the tangent function.
The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, angle B is the angle that is opposite side b and adjacent to side a.
To find the measure of angle B, we can use the formula:
tan(B) = Opposite / Adjacent
Therefore, we can rearrange the formula to solve for B:
B = atan(Opposite / Adjacent)
where "atan" represents the inverse tangent function.
Plugging in the values given in the question, we have:
B = atan(960 / 490)
To calculate this using a calculator, follow these steps:
1. Press the "2nd" or "Shift" key.
2. Press the "TAN" or "Tan-1" key. This will activate the inverse tangent function on the calculator.
3. Enter the numerator of the ratio (960) and press the division key (/).
4. Enter the denominator of the ratio (490) and press the "=" key.
5. The result you see on the calculator will be the measure of angle B in radians.
6. To convert the result to degrees, multiply it by 180/π (approximately 57.3).
Using a calculator, the measure of angle B to the nearest degree is approximately 63 degrees.