(Gillesania)TRIGONOMETRY SETS 10, 11
A. 60deg
Problem 10-11: If coversine x is 0.134, find the value of x. A. 60deg B. 45deg C. 30deg D. 20deg
B. A + 2B = 30deg
Problem 10-13: If sin3A = cos6B then: A. A + B = 180deg B. A + 2B = 30deg C. A - 2B = 30deg D. A + B = 30deg
A. 3
Problem 10-17: How many different value of x from 0deg to 180deg for the equation (2sin x -1)(cos x +1) = 0 A. 3 B. 0 C. 1 D. 2
D. 0.4
Problem 10-20: If sec(A)^2 is 5/2, the quantity 1-sin(A)^2 is equivalent to: A. 2.5 B. 0.6 C. 1.5 D. 0.4
A. 1 & -5/13
Problem 10-21: Find sinx if 2sinx + cosx -2 = 0 A. 1 & -5/13 B. -1 & 5/13 C. 1 & 5/13 D. -1 & -5/13
B. 0.250
Problem 10-23: If sinA = 2.571x, cosA = 3.06x, and sin 2A = 3.939x, find the value of x. A. 0.350 B. 0.250 C. 0.100 D. 0.150
D. 0
Problem 10-27: If (sin x + 1)/sin x = 2^1/2, then (sin(x)^2 +1)/sin(x)^2 is equal to: A. 2^1/2 B. 1 C. 2 D. 0
C. a conditional equation
Problem 10-28: The equation 2sinx + 2cosx - 1 = 3^1/3 A. an identity B. a parametric equation C. a conditional equation D. a quadratic equation
C. cot x
Problem 10-29: If x + y = 90deg, then (sinxtany)/(sinytanx) is equal to: A. tan x B. cos x C. cot x D. sin x
D. (2x^2 -4) / x^2
Problem 10-30: If cos(teta) = x/2 then 1 - tan(teta)^2 is equal to: A. (2x^2 + 4) / x^2 B. (4 - 2x^2) / x^2 C. (2x^2 - 4) / x D. (2x^2 - 4) / x^2
C. 90deg
Problem 10-3: The sum of the two interior angles of the triangle is equal to the third angle and the difference of the two angles is equal to 2/3 of the third angle. Find the third angle. A. 15deg B. 75deg C. 90deg D. 120deg
C. cos 3x - sin 3x
Problem 10-40: Which of the following is different from the others? A. 2cos2x - 1 B. cos4x - sin4x C. cos3x - sin3x D. 1 - 2sin2x
B. 2^1/2 times
Problem 10-47: In an isosceles right triangle, the hypotenuse is how much longer than its side? A. 2 times B. 2^1/2 times C. 1.5 times D. none of these
B. 2 mils
Problem 10-48: Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards. A. 2.5 mils B. 2 mils C. 4 mils D. 1 mil
B. 4.72degrees
Problem 10-49: The angle or inclination of ascend of a road having 8.25% grade is ________ degrees A. 5.12degrees B. 4.72degrees C. 1.86degrees D. 4.27degrees
D. 43deg
Problem 10-6: Solve for x: sinx - secx + cscx - tan2x = -0.0866 A. 40deg B. 41deg C. 47deg D. 43deg
D. x
Problem 10-8: Given three angles A, B, and C whose sum is 180deg. If the tanA + tanB + tanC = x, find the value of tanA x tanB x tanC A. 1-x B. x^1/2 C. x/2 D. x
D. 14.3
Problem 11-10: If AB = 15m, BC = 18m and CA = 24m, find the point intersection of the angular bisector from the vertex C. A. 11.3 B. 12.1 C. 13.4 D. 14.3
A. 216 sq.cm
Problem 10-50: The sides of a right triangle is in arithmetic progression whose common difference is 6cm. Its area is: A. 216 sq.cm B. 270 sq. cm C. 360 sq.cm D. 144sq.cm
C. 19.94
Problem 11-15: From a point outside of an equilateral triangle, the distance to the vertices are 10m, 10m, and 18m. Find the dimension of the triangle. A. 25.63 B. 45.68 C. 19.94 D. 12.25
C. after 2.13hours
Problem 11-17: An airplane leaves an aircraft carrier and flies South at 350mph. The carrier travels S 30deg E at 25mph. If the wireless communication range of the airplane is 700 miles, when will it lose contact with the carrier? A. after 4.36hours B. after 5.57hours C. after 2.13hours D. after 4.54hours
B. 2 x 5^1/2 meters
Problem 11-18: A statue 2 meters high stands on a column that is 3 meters high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue? A. 5 x 2^1/2 meters B. 2 x 5^1/2 meters C. 20 meters D. 10^1/2 meters
B. 12493
Problem 11-21: From a point A at the foot of the mountain, the angle of elevation of the top B is 60deg. After ascending the mountain one (1)mile at an inclination of 30deg to the horizon and reaching a point C, an observer finds that the angle ACB is 135deg. The height of the mountain in feet is: A. 14386 B. 12493 C. 11672 D. 11225
A. 4.72deg
Problem 11-22: A 50-meter vertical tower casts a 62.3-meter shadow when the angle of elevation of the sun is 41.6deg. The inclination of the ground is: A. 4.72deg B. 4.33deg C. 5.63deg D. 5.17deg
B. 11 meters
Problem 11-23: A vertical pole is 10 m from a building. When the angle of elevation of the sun is 45deg, the pole cast a shadow on the building 1m high. Find the height of the pole. A. 0 meter B. 11 meters C. 12 meters D. 13 meters
C. 47.9
Problem 11-2: A truck travels from point M northward for 30min then eastward for one hour, then shifted N 30deg W. If the constant speed is 40kph, how far directly from M, in km will be it after 2 hours? A. 43.5 B. 45.2 C. 47.9 D. 41.6
C. P601,650.00
Problem 11-30: A rectangular piece if land 40m x 30m is to be crossed diagonally by a 10-m wide roadway as shown. If the land cost P1,500.00 per square meter the cost of the roadway is: A. P401.10 B. P60,165.00 C. P601,650.00 D. P651,500.00
A. 0.5 sq. m
Problem 11-31: A man improves a temporary shield from the sun using a triangular piece of wood with dimension of 1.4m, 1.5m, and 1.3m. With the longer side lying horizontally on the ground, he props up the other corner of the triangle with a vertical pole 0.9m long. What would be the are of the shadow on the ground when the sum is vertically overhead? A. 0.5 sq. m B. 0.75 sq. m C. 0.84 sq. m D. 0.95 sq. m
A. 9.17 inches
Problem 11-33: A clock has a dial face 12 inches in radius. The minute hand is 9 inches long while the hour hand is 6 inches long. The plane if rotation of the minute hand is 2 inches above the plane of rotation of the hour hand. Find the distance between the tips of the hand at 5:40AM A. 9.17 inches B. 8.23 inches C. 10.65 inches D. 11.25 inches
C. 15.56deg
Problem 11-35: A plane hillside is inclined at angle of 28deg with the horizontal. A man wearing skis can climb this hillside by following a straight path inclined at an angle of 12deg to the horizontal, but one without skis must follow a path inclined at an angle of only 5deg with the horizontal. Find the angle between the directions of the two points. A. 13.21deg B. 18.74deg C. 15.56deg D. 17.22deg
C. 4p.m.
Problem 11-38: If the time is 8:00 a.m. GMT, what is the time in the Philippines, which is located at 120deg East longitude? A. 6 p.m. B. 4 a.m. C. 4 p.m. D. 6 a.m.
A. 2.87 hours
Problem 11-39: An airplane flew from Manila (14deg 36' N, 121deg 05'E) at a course of S 30deg E maintaining a certain altitude and following a great circle path. If its groundspeed is 350 knots, after how many hours will it cross the equator? A. 2.87 hours B. 2.27 hours C. 3.17 hours D. 3.97 hours
D. 6046.2 nautical miles
Problem 11-40: Find the distance in nautical miles between Manila and San Francisco. Manila is located at 14deg 36' N latitude and 121deg 05'E longitude. San Francisco is situated at 37deg 48'N latitude and 122deg 24'W longitude. A. 7856.2 nautical miles B. 5896.2 nautical miles C. 6326.2 nautical miles D. 6046.2 nautical miles
D. 101.85 m
Problem 11-41: A at certain point in the ground, the tower at the top of 20-m high building subtends an angle of 45deg. At another point in the ground 25 m closer the building, the tower subtends an angle of 45deg. find the height of the tower? A. 124.57 m B. 87.45 m C. 154.32 m D. 101.85 m
B. 93.74
Problem 11-8: Two sides of a triangle are 50m and 60m long. The angle included between these sides is 30degrees. What is the interior angle (in degrees) opposite the longest side? A. 92.74 B. 93.74 C. 94.74 D. 91.74
C. 4.73 cm
Problem 11-9: These sides of a triangle ABC are AB = 15cm, BC = 18cm, and CA = 24cm. Determine the distance from the point of intersection of the angular bisectors to side AB. A. 5.21 cm B. 3.78 cm C. 4.73 cm D. 6.25 cm