Pet 3 Trigo-plane-solid Geom

PET 2 TRIGONOMETRY, PLANE and SOLID GEOMETRY

1. If the time is 8:00 AM GMT, what is time in a country located 150° West longitude? A. 6 PM B. 10 AM C. 6 AM D. 10 PM * 2. The Leaning Tower of Pisa currently “leans” at a 4  angle and has a vertical height of 55.86 meters. How tall was the tower when it was originally built? A. 59 B. 57 C. 58 D. 56 * ∘

3. An engineer desires to measure the height of a tower by observing a vertical angle at A. He then moves 54m further towards the tower at B and observes the vertical angle to be twice that of A. He again proceeds to move further towards the tower at C still on the same line at a distance of 21 m. The observed vertical angle of the tower at this point is three times that at A. Determine the angle of elevation of the tower at A. A. 38°11’ B. 24°35’ C. 26°76’ D. 19°05’ * 19°05’  * 4. A. B. C. D.

Find the equivalent expression of tan(x) + cot(x) cos(x)sin(x) sec(x)csc(x)* cot(x)tan(x) cos(x)tan(x)

5. A sphere of radius 10m and a right circular cone of base radius 10m and height 15m stands on a table. At what height from the table should the solid be cut in order to have equal circular sections? A. 3.33 m B. 3.44 m C. 3.54 m * D. 3.64 m

6. A certain angle has a supplement five times the compliment. Find the angle. A. 168.5 B. 157.5 C. 67.5 * D. 186 7. A right spherical triangle has an angle C=90°, a=50°, and c=80°. Find the side. A. 45.33° B. 78.66° C. 74.33° * D. 75.89° 8. The distance between the centers of the circles which are mutually tangent to each other externally are 10 cm, 12 cm, and 14 cm respectively. Find the area of the largest circle. A. 201.06 cm2 * B. 213.10 cm2 C. 253.94 cm2 D. 251.86 cm2 9. A ship leaves port with a bearing of N 63° W. After travelling 25 miles, the ship then turns 90° and travels on a bearing of S 27° W for 24 miles. At that time, what is the bearing of the ship from the port? A. S 73.2° W * B. W 73.2° S C. S 73.2° E D. E 73.2° S 10. A rectangular tablecloth costs P130. A similar table cloth is five times longer and five times wider. How much would you pay expect to pay for the table cloth? A. P3,250 * B. P1,300 C. P1,950 D. P650 11. In triangle ABC, right-angled at C, tanA + tanB is equal to A. a + b B. (c^2)/ab * C. (a^2)/bc D. (b^2)/ac

12. The slant height of a right circular cone is 5m long. The base diameter is 6m. What is the total surface area in sq. m? A. 12 pi B. 15 pi C. 24 pi * D. 30 pi 13. A vertical pole is 10 m from a building. When the angle of elevation of the sun is 45°, the pole cast a shadow on the building 1m high. Find the height of the pole. A. 10 m B. 11 m * C. 12 m D. 13 m 14. The space diagonal of a cube (the diagonal joining two noncoplanar vertices) is 6m. The total surface area of the cube is: A. 72 * B. 66 C. 60 D. 78 15. The perimeter of rectangle PQRS is 4P feet. What is the perimeter, in inches, of a rectangle whose length and width are one half the length and width of rectangle PQRS? A. P B. 2P C. 12P D. 24P *