In ΔPQR, side PR = 43.0 cm, ∠PQR = 28.0o, and ∠QPR= 26.0o. Determine the length of side…
- User
In ΔPQR, side PR = 43.0 cm, ∠PQR = 28.0o, and ∠QPR= 26.0o.
Determine the length of side QR in centimetres to one decimal place.
- Assistant
Using the Law of Sines, we can set up an equation in the form of:
QR/sin(∠P) = PR/sin(∠Q)
First, let's find the value of ∠P in ΔPQR. We know that the sum of angles in a triangle is 180°, so
∠P = 180° - 28.0° - 26.0° = 126°
Now we can use the Law of Sines:
QR / sin(126°) = 43 cm / sin(28.0°)
Now we can solve for QR:
QR = (43 cm * sin(126°)) / sin(28.0°) QR ≈ 63.1 cm
The length of side QR is approximately 63.1 cm.
- User
Bob is pulling on a rope with a force of 588 N at an angle of elevation θ = 35.0o. Determine the horizontal component of the force in newtons to one decimal place.
- Assistant
To find the horizontal component of the force, we can use the equation:
Horizontal Component = Force * cos(θ)
θ = 35.0°, and the force being applied is 588 N. Therefore,
Horizontal Component = 588 N * cos(35.0°) ≈ 481.6 N
The horizontal component of the force is approximately 481.6 N.