A lighthouse stands 475 m off a straight shore and the focused beam of its light revolves four times each minute. As shown in the​ figure, P is the point on shore closest to the lighthouse and Q is a point on the shore 200 m from P. What is the speed of the beam along the shore when it strikes the point​ Q? Describe how the speed of the beam along the shore varies with the distance between P and Q. Neglect the height of the lighthouse.

Q: 8. Two planes take off at the same time from an airport. The first plane is flying at 255 miles per…

A: If there are no wind currents blowing, we have to find how far apart are they after 2 hours. andWe…

Q: 3. Lompoc, California, is 18 miles due south of Nipomo. Buellton, California, is due east of Lompoc…

A: Given:       Lompoc is 18 miles due south of Nipomo.       Buellton is due east of Lompoc and S 65°…

Q: Calculate the height of the two buildings in the figure.

A: In a right angled triangle, the tangent of an angle is given by :…

Q: What is the linear speed of the tip on one of the blades in feet per second?

A: Given that the blender can spin up to 24,000 rpm. That is, ω≤24000 rpm≤24000×2π60 rad/sec≤800π…

Q: Convert ( 4, 4 to Cartesian coordinates. Give exact answers (no decimals or trig functions).

A: The given polar coordinates is 4, π4. Here, r=4 and θ=π4. The following formulae are used to convert…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.