Chapter 7

In the following problems, the magnitudes \(A\) and \(B\) of two perpendicular vectors are given. Find the resultant and the angle that it makes with \(B\) $$A=46.8 \quad B=38.6$$

Evaluate the following, giving your answer in decimal degrees to three significant digits. $$\cos ^{-1} 0.229$$

Sketch each right triangle and find all missing parts. Work to three significant digits and express the angles in decimal degrees. $$a=63.9 \quad b=84.3$$

In the following problems, the magnitudes \(A\) and \(B\) of two perpendicular vectors are given. Find the resultant and the angle that it makes with \(B\) $$A=1.25 \quad B=2.07$$

After leaving port, a ship holds a course \(\mathrm{N} 46^{\circ} 12^{\prime} \mathrm{E}\) for 225 mi. Find how far north and how far east of the port the ship is now located.

Evaluate the following, giving your answer in decimal degrees to three significant digits. $$\arctan 4.26$$

A circuit has an impedance of \(975 \Omega\) and a phase angle of \(28.0^{\circ} .\) Find the resistance and the reactance.

In the following problems, the magnitudes \(A\) and \(B\) of two perpendicular vectors are given. Find the resultant and the angle that it makes with \(B\) $$A=274 \quad B=529$$

Sketch each right triangle and find all missing parts. Work to three significant digits and express the angles in decimal degrees. $$b=746 \quad c=957$$

A circuit has a reactance of \(5.75 \Omega\) and a resistance of \(4.22 \Omega .\) Find the magnitude of the impedance and the phase angle.

In the following problems, the magnitudes \(A\) and \(B\) of two perpendicular vectors are given. Find the resultant and the angle that it makes with \(B\) $$A=6.82 \quad B=4.83$$

A certain roof has a rise of 9 in a run of \(12 .\) What angle does it make with the horizontal?

Sketch each right triangle and find all missing parts. Work to three significant digits and express the angles in decimal degrees. $$a=41.3 \quad c=63.7$$

In the following problems, the magnitudes \(A\) and \(B\) of two perpendicular vectors are given. Find the resultant and the angle that it makes with \(B\) $$A=58.3 \quad B=37.2$$

Sketch each right triangle and find all missing parts. Work to three significant digits and express the angles in decimal degrees. $$a=4.82 \quad b=3.28$$

In the following problems, the magnitudes \(A\) and \(B\) of two perpendicular vectors are given. Find the resultant and the angle that it makes with \(B\) $$A=2.27 \quad B=3.97$$

A guy wire \(82.0 \mathrm{ft}\) long is stretched from the ground to the top of a telephone pole \(65.0 \mathrm{ft}\) high. Find the angle between the wire and pole.

Sketch each right triangle and find all missing parts. Work to three significant digits and express the angles in decimal degrees. $$a=274 \quad c=429$$

Using CAD, (1) draw a right triangle, and label one acute angle as \(\theta ;\) (2) have the program measure each side, and compute and display the ratios of the sides, as related to \(\theta ;\) (3) using the built-in trigonometric functions, compute and display the sine, cosine, and tangent of \(\theta ;\) (4) compare these to the ratios of the sides computed in step \(2 ;(5)\) drag a vertex of the triangle, making sure it stays a right triangle, and observe the new values. What do you conclude?

Two of the sides of an isosceles triangle have a length of 150 units, and each of the base angles is \(68.0^{\circ} .\) Find the altitude and the base of the triangle.

Find the length of a side of regular hexagon inscribed in a 125 -cm-radius circle.

Bolt circle: A bolt circle with a radius of \(36.000 \mathrm{cm}\) contains 24 equally spaced holes. Find the straight-line distance between the holes.

Project: In The Musgrave Ritual, Sherlock Holmes calculates the length of the shadow of an elm tree that is no longer standing. He does know that the elm was 64 ft high and that the shadow was cast at the instant that the sun was grazing the top of a certain oak tree. Holmes held a \(6-\) ft-long fishing rod vertical and measured the length of its shadow at the proper instant. It was 9 ft long. He then said, "Of course the calculation now was a simple one. If a rod of six feet threw a shadow of nine, a tree of sixty-four feet would throw one of _____ "How long was the shadow of the elm?