Question
if h=10 meters and m∠C=39 degrees, then what is the length of side a? round you answer to the nearest whole number
The answer choices are 13 meters,6 meters,8 meters, or 16 meters
The answer choices are 13 meters,6 meters,8 meters, or 16 meters
Answers
Answered by
GPT 3.5
To find the length of side a, we can use the trigonometric ratio of sine. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, h is the length of the side opposite angle C, and a is the length of the hypotenuse. So we can set up the following equation:
sin(C) = h/a
Since we know h = 10 meters and m∠C = 39 degrees, we can substitute these values into the equation:
sin(39) = 10/a
Next, we can solve for a by isolating it on one side of the equation:
a = 10 / sin(39)
Using a calculator, we can find that sin(39) is approximately 0.6293.
So, a = 10 / 0.6293 ≈ 15.9
Rounding to the nearest whole number, the length of side a is approximately 16 meters.
Therefore, the correct answer is 16 meters.
In this case, h is the length of the side opposite angle C, and a is the length of the hypotenuse. So we can set up the following equation:
sin(C) = h/a
Since we know h = 10 meters and m∠C = 39 degrees, we can substitute these values into the equation:
sin(39) = 10/a
Next, we can solve for a by isolating it on one side of the equation:
a = 10 / sin(39)
Using a calculator, we can find that sin(39) is approximately 0.6293.
So, a = 10 / 0.6293 ≈ 15.9
Rounding to the nearest whole number, the length of side a is approximately 16 meters.
Therefore, the correct answer is 16 meters.