The hypotenuse of the right triangle PQR is 16ft. length. The sine of the angle <P is 3/5. How many feet long is the line if QR?
sin P = QR/16
3/5 = QR/16
QR = 16(3/5) = 9.6
To find the length of line QR, we can use the sine function since we have the sine of angle P.
Using the sine function, we know that sin(θ) = opposite/hypotenuse.
In this case, sin(P) = QR/16.
Given that sin(P) = 3/5, we can set up the equation:
3/5 = QR/16.
To solve for QR, we can cross multiply:
5 * QR = 3 * 16.
Now, we can simplify the equation:
5 * QR = 48.
Dividing both sides by 5:
QR = 48/5.
QR is approximately equal to 9.6 ft.
Therefore, the line QR is approximately 9.6 ft long.
To find the length of QR, we need to use the sine ratio in trigonometry. The sine ratio relates the length of the side opposite an angle to the length of the hypotenuse of a right triangle.
In this case, we are given the sine of angle P, which is sin(P) = 3/5. We can use this information to find the length of the side QR.
The sine of an angle is calculated by dividing the length of the side opposite the angle by the length of the hypotenuse. So, we have the equation:
sin(P) = QR / PQ
To solve for QR, we can rearrange the equation:
QR = sin(P) * PQ
We are given that PQ is the length of the hypotenuse and it is 16 ft. Substituting this value into the equation, we have:
QR = (3/5) * 16
Now, let's calculate QR:
QR = (3/5) * 16
= (3 * 16) / 5
= 48 / 5
= 9.6 ft
Therefore, the length of line QR is 9.6 feet.