A rain gutter is to be constructed from a metal sheet ofwidth 30 cm by bending up one-third of the sheet on eachside through an angle theta  . How should theta  be chosen so that thegutter will carry the maximum amount of water?

Q: The law of cosines generalizes the Pythagorean theorem. True or false?

A: Law of cosine is

Q: Prove that an object thrown at an acute angle of elevation travels along a parabolic path, if wind…

A: To show that the path is parabolic                 ux=u cos θuy=u sin θax=0ay=±g

Q: A string of a kite is 180 meters long and it makes an angle of 75° with horizontal. Find the height…

A: use trignometric ratio

Q: What is the vertical component of the ball's location, after it has spun through an angle of…

A:

Q: A rope is attached to the bottom of a hot-air balloon that is floating above a flat field. If the…

A: Given: The angle of elevation of the balloon is 65°, and the rate of pulling of rope is 5 ft /s.…

Q: In AHIJ, the measure of J=90°, IH = 65, HJ = 56, and JI = 33. What is the %3D %3D value of the sine…

A: First sketch a triangle for the given measures as shown below.

Q: A plane flies due west for 2 hr then due south for 1 hr at an average speed of 375 mph. To the…

A:

Q: At what rate is the angle between a clock’s minute and hour hands changing at 4 o’clock in the…

A:

Q: A cable man is looking down from the top of a telephone pole at an angle of 14°. The pole is 30 feet…

A: where , x= horizontal distance from the bottom of the pole

Q: 3. Find the six circular functions of the angle e generated by an arc with a length equal to .

A:

Q: A force of 745 pounds just keeps a 4100 - pound vehicle from rolling down a hill. To the nearest…

A:

Q: A ladder that is 16 foot long liens against a vertical wall such that it’s based makes a 60° angle…

A:

Q: An airplane is flying at an altitude of 11,000 feet. The pilot wants to make a smooth final descent…

A: Given that, altitude = 11,000 feet angle of depression = 5 degree.

Q: A rock is thrown downward from the top of a building, 168 ft high, at an angle of 60 ◦ with the…

A: Use the displacement formula, x=v0(cos θ)t and substitute v0 with 80 and θ with 60° to get x=40t.…

Q: Consider a right triangle with a side of length x opposite angle AA, a side of length yy opposite…

A:

Q: A Russian bomber plane is sighting on a target on the ground directly ahead. If the bomber is flying…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A volleyball is hit when it is 4 ft above the groundand 12 ft from a 6-ft-high net. It leaves the…

A: Explanation: Firstly we will draw the diadram                                According to the…

Q: A woman is watching a launched rocket currently 13 miles in altitude. If she is standing 3 miles…

A: The given information ( Rocket altitude = 13 miles and women standing at 3 miles from the launchpad…

Q: Suppose that you are headed toward a plateau 21 meters high. If the angle of elevation to the top of…

A: Let’s analyse the given information pictorially.

Q: Let a = ci + jand b = 3i + 4j. Find c so that the angle between a and b is %3D Round your answers to…

A: Given a = ci + j and b = 3i + 4j. The angle between a and b is π6. We have to find the value of c.

Q: A man standing on a 45m building high, has an eyesight height of 1.5m from the top of the building,…

A:

Q: A helicopter is to fly directly from a helipad at the origin in the directionof the point (1, 1, 1)…

A: Given that: A helicopter is to fly directly from a helipad at the origin in the direction of the…

Q: When it was constructed 4,500 years ago, the Great Pyramid in Egypt had a height of 147 meters and…

A:

Q: A 100-foot vertical tower is to be erected on the side of a hill that makes a 6° angle with the…

A:

Q: use the formula x=1/32 v2 sin 2 theta to explain why the projection angle that maximizes the…

A:

Q: a bird is sitting in the top of a tree that is 21 feet tall looking down at a worm on the ground…

A:

Q: Find the six circular functions of the angle 0 generated by am 11n arc with a length equal to 6.

A: Given,  Arc length,  S=11π6 θ=Sr If we take r=1,  We get, θ=S Hence, θ=11π6radians or 330°

Q: A kite is flying at an angle of elevation of about 40°. All 80 m of stringhave been let out.…

A:

Q: • A Statue 10m high is standing on a base of 2m high, If an observer's eye is 1.2 m above the…

A:

Q: against

A:

Q: The figure shows a 200-foot tower on the side of a hill that forms a 5° angle with the horizontal.…

A:

Q: The figure shows a 450 foot tower on the side of a hill that forms a 8° angle with the horizontal.…

A:

Q: A 100-foot vertical tower is to be erected on the side of a hill that makes a 6° angle with the…

A: ANSWER IS AS FOLLOWS:

Q: A string of a kite is 100 meters long and it makes an angle of 60° with horizontal. Find the height…

A:

Q: A large nest of recently hatched bald eagles is located at the top of the Eiffel Tower (which is 324…

A: Given: Eiffel Tower is 324 meters tall The tourist standing 54 meters away from Eiffel Tower Find…

Q: From a point on level ground 125 feet from the base of a tower, the angle ofelevation is 57.2°.…

A: let a represents the height of the tower. In the right triangle, we have a known angle, an unknown…

Q: The pilot of a small airplane flying 300 m above the ground notices a village off the left wing at a…

A:

Q: A cannon is fired at an angle of 39° with the horizontal. If the cannonball has an initial velocity…

A: The angle of projectile from the launch is given as 39° The initial velocity is given as 605 ft/s…

Q: An airplane climbs at an angle of 11 degrees at an average apees of 420 mph. How long will it take…

A:

Q: While standing at the left corner of the schoolyard in front of her school, Suzie estimates that the…

A:

Q: From the top of a building at 87.sm, Super Barn Sees his neighbor yekkó the Yak Sitting by his Yert…

A: Given:- From the top of a building at 87.8m, Super Barry Sees his neighbour Yekkó the Yak Sitting by…

Q: Sun 10.5ft. 24°

A:

Q: A river has a constant current of 3 kilometers per hour. At what angle to a poat dock should a…

A:

Q: A hot-air balloon is held at a constant altitude by two ropes that are anchored to the ground. One…

A: find the distance in the following way:-

Q: How does the law of cosines generalize the Pythagorean theorem?

A: We have to show that the law of cosines generalize the Pythagorean theorem.

Q: Sally has measured the end-points of two poles, and wants to know the angle between them: Use the…

A: Given, a= 10,3,9 and b=3,8,12 To find : Angleθ between two vectors a→ and b→

Q: Find

A: Given that : Diameter = 30 feet Radius = 15 feet Length = 2 feet Inclination = 45 degrees

Q: A force of 13 lb is required to hold a 29-lb crate on a hill. What angle does the hill make with the…

A: To calculate the angle which is make with the horizontal if the force acting on an object is 13 lb…

Q: At what minimum height above ground level must I place a satellite dish so that, when pointed upward…

A: According to the question:

Q: At what rate is the angle between a clock's minute and hour hands changing at 7 o'clock in the…

A: To find: Rate of change of angle between a clock's minute and hour hand at 7 AM. In other words, the…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.