TRIGONOMETRY

TRIGONOMETRY

1. Find the length of the hypotenuse of the triangle whose sides are 4 cm and 6 cm.2. Find the length of the side of the triangle if its hypotenuse is 6 cm and one side 3 cm3. Convert 240 to radians4. Convert 3/8 to degrees5. One day you stroll down the river and take a walk along the river bank. At one point in time you notice a rock directly across from you. After walking 100 feet downstream you now have to turn an angle of 32 with the river to be looking directly at the rock. How wide is the river?6. Use the sum formula for the cosine function to find the exact value for cos(75)7. Find the area of a triangle whose sides a,b and c are 9,20 and 17 respectively. 8. In the triangle shown, fill in the missing information

9. If sin = 12/13, and cos = 5/13, then tan = ?10. From a hot air baloon, the angle between a radio antenna straight below and the base of the library downtown is 57. If the distance between the radio antenn and the library is 1.3 miles, how many miles high is the baloon?11. Simplify 12. . Asurveyor wishes to determine the height of a building. He measures a distance of 1500 feet along the ground from the building, and there he determines the angle of elevation to the top of the building. This angle is 24. How tall is the building?13. A ladder 9m long is placed against a building. The angle between the ladder and the ground is 65. How high up is the top of the ladder?14. Compute the angles in a triangle with sides 18m, 13m, and 13m long15. There is a 26-mile pathway towards the ocean, perpendicular to the beach. Two runners agree to race on this path. The rst runner runs the path with a perfect accuracy. The second runner misses the perpendicular path by 1.5 to the right. a) How far are apart are the endpoints of the runnerspaths? b) How much more did the second runner run than the rst runner, due to the inaccuracy of the path?16. From a hot air balloon that is 500m high, the angles of depression to two houses, in line with the balloon, are 38 and 49. How far apart are the houses17. A regular polygon of 12 sides is written into a circle of radius 5ft. Find the area of the polygon.18. Find the angle that is formed by the positive part of the x-axis and the straight line 2x+5y = 1. 19. The angle of elevation to the top of a building changes from 12 to 25 as the observer travels 200m towards the building. How tall is the building?20. A kite ies over a fence and starts to descend. The person holding the string attached to the kite is holding it one meter above the ground. The fence is two meters high at a distance of 4 meters from the person. At the instant the kite touches the fence, there is 3 meters of string between the kite and the fence. At that instant, how high o the ground is the kite?21. Convert the following angle to radians: 4522. A boy flying a kite lets out 300 feet of string which makes an angle of 38 with the ground. Assuming that the string is straight, how high above the ground is the kite? 23. A ladder leaning against the wall makes an angle of 74with the ground. If the foot of the ladder is 6.5 feet from the wall, how high on the wall is the ladder? 24. A straight road to the top of a hill is 2500 feet long and makes an angle of 12 with the horizontal. Find the height of the hill.25. An airplane climbs at an angle of 11 with the ground. Find the ground distance it has traveled when it has attained an altitude of 400 feet. 26. A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and makes an angle of 58 with the ground. Find the length of the wire. 27. Henry is flying a kite. The kite string makes an angle of 43 with the ground. If Henry is standing 100 feet from a point on the ground directly below the kite, find the length of the kite string. 28. A 25 foot ladder leans against a building. The ladders base is 13.5 feet from the building. Find the angle which the ladder makes with the ground.29. In order to reach the top of a hill which is 250 feet high, one must travel 2000 feet straight up a road which leads to the top. Find the number of degrees contained in the angle which the road makes with the horizontal. 30. In the new Comiskey Park,the home of the Chicago White Sox baseball team, the first row of seats in the upper deck is farther away from home plate than the last row of seats in the old Comiskey Park.Although there is no obstructed view in the new park, some of the fans still complain about the present distance from home plate to the upper deck of seats. From a seat in the last row of the upper deck directly behind the batter, the angle of depression to home plate is 29.9, and the angle of depression to the pitchers mound is 24.2. Find (a) the viewing distance to home plate and (b) the viewing distance to the pitchers mound.31. Find two positive and two negative angles that are coterminal with (a) 51and (b) -7.32. Multiply and simplify 33. Factor and simplify 34. Add and simplify 35. Multiply and simplify 36. Through the Mentoring in the City Program sponsored by Marian College, in Indianapolis, Indiana, children have turned a vacant downtown lot into a monument for peace.* This community project brought together neighborhood volun- teers,businesses,and government in hopes ofshowing children how to develop positive, nonviolent ways of dealing with conflict. A landscape architect used the childrens drawings and ideas to design a triangular- shaped peace garden. Two sides of the property, formed by Indiana Avenue and Senate Avenue,measure 182 ft and 230 ft,respectively,and together form a 44.7 angle. The third side of the garden, formed by an apartment building, measures 163 ft. What is the area of this property?37. Solve ABC if a=32, c=48 and B=152.238. Solve RST if r=3.5, s=4.7and t=2.839. Logan and Cassidy leave a campsite, Logan biking due north and Cassidy biking due east. Logan bikes 7 km/h slower than Cassidy. After 4 hr, they are 68 km apart. Find the speed of each bicyclist. 40. Solve in [0,360]41. Solve in [0,2]

42. During a rescue mission,a Marine fighter pilot receives data on an unidentified aircraft from an AWACS plane and is instructed to intercept the aircraft. The diagram shown appears on the screen, but before the distance to the point of interception appears on the screen, communications are jammed. Fortunately, the pilot remembers the law of sines. How far must the pilot fly?

43. Knifemakers know that the bevel of the blade (the angle formed at the cutting edge of the blade) determines the cut- ting characteristics of the knife. A small bevel like that of a straight razor makes for a keen edge, but is impractical for heavy-duty cutting because the edge dulls quickly and is prone to chipping.A large bevel is suitable for heavy-duty work like chopping wood. Survival knives, being univer- sal in application, are a compromise between small and large bevels. The diagram at left illustrates the blade of a hand-made Randall Model 18 sur- vival knife.What is its bevel?

44. Find the trigonometric notation for the compex number 1+i45. Find the trigonometric notation for the complex number 46. A wheel of a car of radius 21 cms is rotating at 600 RPM. What is the speed of the car in km/hr? 47. Two sides of a triangle is 8 cm and 12 cm. Find its area if its perimeter is 26 cm.48. If A is acute and , determine the values of the remaining functions.49. From a point A on level ground, the angles of elevation of the top D and bottom B of a flagpole situ ated on the top of a hill are measured as 4754 and 3945. Find the height of the hill if the height of the flagpole is 115.5 ft.50. From the top of a lighthouse, 175 ft above the water, the angle of depression of a boat due south is 1850. Calculate the speed of the boat if, after it moves due west for 2 min, the angle of depression is 1420

SOLID MENSURATION

1. A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted? 2. The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr? 3. A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year? 4. The length of a rope, to which a cow is tied, is increased from 19m to 30m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. 5. A cube of edge a is cut by a plane containing two diagonally opposite edges of the cube. Find the area of the section thus formed.6. A storage room has a rectangular floor 76 ft by 42 ft. The walls are vertical and 20 ft high. If there are no windows , find the total area of the ceiling, walls, and floor. Also find the storage space of the room.7. A masonry dam 40 ft high has a uniform vertical cross section as shown in the figure. The dam is 80 ft long and its material weighs 125 lb. Per cu.ft. Find the weight of the dam.

8. An iron pipe 10 ft long has an internal diameter of 1 ft. If the iron is 1/2 in. Thick, find the volume of metal in the pipe..9. Find the are of the largest circle which can be cut from a square of edge 4 in, what is the area of the material wasted?10. A garden plot is to contain 200 sq ft. If its length is to be twice its width, what should its dimension be?

11. Find th perimeter and area of the shape below

12. Find the are of the door shown in the figure in the right.The top part of the door is a semicircle

13. A sleeping policeman(traffic calming road bump) is made of concrete and has the dimensions shown in the diagram. Find the volume of concrete needed to make one.

14. Find the lateral surface area of a cylinder whose circumference is 44 cm and height 10 cm.15. The lateral surace area of a thin circular botommed tin is 1760 sq. cm and radius is 10 cm. What is the height of the tin?16. Find he volume of the cylinder whose radius is 7 cm and height is 12 cm17. Calculate the curved surface area of cone, given radius of the base as 10 cm. And slant height 28 cm18. The diameter of a cone is 10 cm and height is 12 cm. Calculate the total surface area of the cone.19. The surface area of the sphere is 616 sq.cm. Find the diameter of the sphere.20. Total volume of 21 steel balls in a bearing is 88cc. Find the diameter of each ball.21. In a bulding there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4m. Find the total cost of painting the curved surface area of all pillars at the rate of $8 per sq.m22. Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 sq.cm?23. A rectngular piece of paper 11 cm x 4 cm is folded without overlapping to make a cylinder of height 4cm. Find the volume of the cylinder.24. An aquarium is in the form of a cuboid whose external measures are 80cm x 30cm x 40cm. The base, side faces and back face are to be covered with a colored paper. Find the area of the paper needed?25. The liquid content of a glass is in the form of a cone of base diameter 3 in. If the glass contains 10 fluid oz., and 1 fluid oz=1.805 cu.in, what is the greatest depth of the liquid?

LYCEUM OF THE PHILIPPINES UNIVERSITYCOLLEGE OF ENGINEERING, COMPUTER STUDIES AND ARCHITECTUREDEPARTMENT OF ENGINEERING AND ARCHITECTURE

SPECIAL TOPICS

PROBLEM SET IN TRIGONOMETRY AND SOLID MENSURATION

SUBMITTED BY:BATERBONIA CHRISTINE B.ECE-501

SUBMITTED TO:ENGR. ARNEL AVELINO

DATE:07/07/15