91Ó°ÊÓ

In Exercises \(7-14,\) with the given sets of components, find \(R\) and \(\theta\). $$R_{x}=7.627, R_{y}=-6.353$$

Solve the triangles with the given parts. $$a=1.13, b=0.510, C=77.6^{\circ}$$

Solve the triangles with the given parts. $$a=0.130, A=55.2^{\circ}, B=117.5^{\circ}$$

Solve the given problems. To move forward, a helicopter pilot tilts the helicopter forward. If the rotor generates a force of 3200 lb, with a horizontal component (thrust) of 420 lb, what is the vertical component (lift)?

Solve the triangles with the given parts. $$b=4384, B=47.43^{\circ}, C=64.56^{\circ}$$

Solve the given problems. The acceleration (a vector quantity) of gravity on a sky diver is \(9.8 \mathrm{m} / \mathrm{s}^{2} .\) If the force of the wind also causes an acceleration of \(1.2 \mathrm{m} / \mathrm{s}^{2}\) at an angle of \(15^{\circ}\) above the horizontal, what is the resultant acceleration of the sky diver?

Add the given vectors by using the trigonometric functions and the Pythagorean theorem. $$\begin{aligned} &A=18.0, \theta_{A}=0.0^{\circ}\\\ &B=12.0, \theta_{B}=27.0^{\circ} \end{aligned}$$

Draw the given vectors and find their sum graphically. The magnitude is shown first, followed by the direction as an angle in standard position. $$3.6 \mathrm{cm}, 0^{\circ} ; 4.3 \mathrm{cm}, 90^{\circ}$$

In Exercises \(15-30,\) add the given vectors by using the trigonometric functions and the Pythagorean theorem. $$\begin{aligned} &A=18.0, \theta_{A}=0.0^{\circ}\\\ &B=12.0, \theta_{B}=27.0^{\circ} \end{aligned}$$

Solve the triangles with the given parts. $$b=103.7, c=159.1, C=104.67^{\circ}$$