91Ó°ÊÓ

Height of a climber: A local Outdoors Club has just hiked to the south rim of a large canyon, when they spot a climber attempting to scale the taller northern face. Knowing the distance between the sheer walls of the northern and southern faces of the canyon is approximately 175 yd, they attempt to compute the distance remaining for the climbers to reach the top of the northern rim. Using a homemade transit, they sight an angle of depression of \(55^{\circ}\) to the bottom of the north face, and angles of elevation of \(24^{\circ}\) and \(30^{\circ}\) to the climbers and top of the northern rim respectively. (a) How high is the southern rim of the canyon? (b) How high is the northern rim? (c) How much farther until the climber reaches the top? PICTURE CANT COPY

(5.1) Invercargill, New Zealand, is at \(46^{\circ} 14^{\prime} 24^{\prime \prime}\) south latitude. If the Earth has a radius of \(3960 \mathrm{mi}\) how far is Invercargill from the equator?

Find the phase angle \(\theta\) if the impedance \(Z\) is \(420 \Omega\), and the resistance \(R\) is \(290 \Omega\)

Convert each radian measure to degrees, without the use of a calculator. $$\theta=\frac{5 \pi}{6}$$

The height of an equilateral triangle: \(H=\frac{\sqrt{3}}{2} S\) Given an equilateral triangle with sides of length \(S\), the height of the triangle is given by the formula shown. Once the height is known the area of the triangle can easily be found (also see Exercise 93 ). The Gateway Arch in St. Louis, Missouri, is actually composed of stainless steel sections that are equilateral triangles. At the base of the arch the length of the sides is \(54 \mathrm{ft}\) The smallest cross section at the top of the arch has sides of \(17 \mathrm{ft}\). Find the area of these cross sections.

At carnivals and fairs, the Gravity Drum is a popular ride. People stand along the wall of a circular drum with radius \(12 \mathrm{ft},\) which begins spinning very fast, pinning them against the wall. The drum is then turned on its side by an armature, with the riders screaming and squealing with delight. As the drum is raised to a near-vertical position, it is spinning at a rate of 35 rpm. (a) What is the angular velocity in radians? (b) What is the linear velocity (in miles per hour) of a person on this ride?

A winch is being used to lift a turbine off the ground so that a tractor- trailer can back under it and load it up for transport. The winch drum has a radius of 3 in. and is turning at 20 rpm. Find (a) the angular velocity of the drum in radians, (b) the linear velocity of the turbine in feet per second as it is being raised, and (c) how long it will take to get the load to the desired height of \(6 \mathrm{ft}\) (ignore the fact that the cable may wind over itself on the drum).

One of the four blades on a ceiling fan has a decal on it and begins at a designated "12 o'clock" position. Turning the switch on and then immediately off, causes the blade to make over three complete, counterclockwise rotations, with the blade stopping at the 8 o'clock position. What angle \(\theta\) did the blade turn through? Name all angles that are coterminal with \(\theta\)

Verifying \(s=r \theta\) On a protractor, carefully measure the distance from the middle of the protractor's eye to the edge of the protractor along the \(0^{\circ}\) mark, to the nearest half-millimeter. Call this length " 1 unit"." Then use a ruler to draw a straight line on a blank sheet of paper, and with the protractor on edge, start the zero degree mark at one end of the line, carefully roll the protractor until it reaches 1 radian \(\left(57.3^{\circ}\right),\) and mark this spot. Now measure the length of the line segment created. Is it very close to 1 "unit" long?

Two ships are cruising together on the open ocean at 10 nautical miles per hour. One of them turns to make a \(90^{\circ}\) angle with the first and increases speed, heading for port. Assuming the first ship continues traveling at 10 knots, use a special triangle to find the speed of the other ship if they are 20 mi apart after 1 hr.