ABC- with angles AB, and C and sides AB,BC, and AC, angle B is right 90degree angle, if sin of angle A is 0.5, side BC 8in., what is length of AC
Perhaps you recognized the 30-6-90 triangle (sinØ=1/2 , so Ø=30°)
so just use a simple ratio:
h/2 = 8/1
h = 16
or
sinØ - .5
Ø = 30°
then sin30 = 8/h
h = 8/sin30 = 8/(1/2) = 16
To find the length of AC in the triangle ABC, we can use the trigonometric ratio sine (sin). Given that angle B is a right angle (90 degrees) and the length of side BC is 8 inches, we can use the Pythagorean theorem and the value of sin(angle A) to calculate the length of side AC.
First, let's find the length of side AB using the Pythagorean theorem:
AB^2 = BC^2 - AC^2
AB^2 = 8^2 - AC^2
AB^2 = 64 - AC^2
Since angle B is a right angle, sin(angle A) = opposite/hypotenuse = AB/AC
0.5 = AB/AC
By substituting AB^2 = 64 - AC^2 into the equation, we can solve for AC:
0.5 = √(64 - AC^2) / AC
Cross-multiplying:
0.5 * AC = √(64 - AC^2)
Squaring both sides to eliminate the square root:
0.25 * AC^2 = 64 - AC^2
1.25 * AC^2 = 64
Dividing both sides by 1.25:
AC^2 = 64 / 1.25
AC^2 = 51.2
Finally, taking the square root of both sides:
AC = √51.2
The length of AC is approximately equal to the square root of 51.2 inches.