91Ó°ÊÓ

Solve the triangle

a = 3, b = 4, C = 40$°$

Logan is playing on her swing. One full swing (front to back to front) takes 6 seconds and at the peak of her swing she is at an angle of $42°$with the vertical. If her swing is 5 feet long, and we ignore all resistive forces, build a model that relates her horizontal displacement (from the rest position) after time t.

Find an equation for the circle with center at the point $(-5,1)$and radius 3. Graph this circle.

Area of an ASA Triangle If two angles and the included side are given, the third angle is easy to find. Use the Law of Sines to show that the area K of the triangle with side $a$and angles A, B, and C is

$K=\frac{a^2\sin B\sin C}{2\sin A}$

Finding the Distance to Shore The Willis Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of Lake Michigan, as indicated in the figure on the top right. An observer in a pleasure boat on the lake directly in front of the Willis Tower looks at the top of the tower and measures the angle of elevation as 5°. How far offshore is the boat?

The distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position, which represents a negative direction.

(a) Describe the motion of the object. Be sure to give the mass and damping factor.

(b) What is the initial displacement of the bob? That is, what is the displacement at t = 0?

(c) Graph the motion using a graphing utility.

(d) What is the displacement of the bob at the start of the second oscillation?

(e) What happens to the displacement of the bob as time increases without bound?

Given equation:$d=-30e^{\frac{-0.6t}{80}}\cos (\sqrt{{\left(\frac{2\mathrm{Ï€}}{7}\right)}^2-\frac{0.36}{6400}}t$

When a mass hanging from a spring is pulled down and then released, the motion is called __________ . if there is no frictional force to retard the motion, and the motion is called ______ if there is friction.

If three sides of a triangle are given, the Law of _________ is used to solve the triangle.

Finding the Speed of a Glider From a glider 200 feet above

the ground, two sightings of a stationary object directly in

front are taken 1 minute apart (see the figure). What is the

speed of the glider?

Finding the Grade of a Mountain Trail A straight trail with a uniform inclination leads from a hotel, elevation 5000 feet, to a lake in a valley, elevation 4100 feet. The length of the trail is 4100 feet. What is the inclination (grade) of the trail?