In right triangle ABC, angle A=3, angle B=60, and angle C=90. Find AB with AC is 12 ?
Let r=AB. Since we were given AC=12 and angle B=60, we can use:
sin 60 = 12/r
Solving for r we have:
r = 12/sin 60 = 13.86
To find the length of side AB in a right triangle ABC, we can use the trigonometric function sine.
The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse. In this case, we are given the length of the side adjacent to angle A (AC) and we want to find the length of the side opposite to angle A (AB).
We can set up the equation as follows:
sin(A) = Opposite/Hypotenuse
Since we want to find AB, we rearrange the equation to solve for AB:
AB = sin(A) * AC
Now let's substitute the given values into the equation:
AB = sin(3) * 12
To calculate this value, we need to convert the angle from degrees to radians. Most scientific calculators have a function to switch between degrees and radians.
sin(3) ≈ 0.05234
Now we can calculate AB:
AB ≈ 0.05234 * 12 ≈ 0.628
Therefore, the length of side AB in the right triangle ABC is approximately 0.628.