1 - 1 + cot²2θ =
sec²Î¸
2 - 1 + tan²2θ =
sec²2θ
3 - A man finds the angle of elevation of the top of a tower to be 30°. He walks 85 m nearer the tower and finds its angle of elevation to be 60°. What is the height of the tower?
73.61 m
4 - A man standing on a 48.5 meter building high, has an eyesight height of 1.5m from the top of the building, took a depression reading from the top of another building and wall, which are 50° & 80°
39.49
5 - A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower at 13° and 35° respectively. The height of the
33.51 m
6 - A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole is leaned 15° from the vertical directly towards the sun, determine the length of the pole.
54.23 m
7 - A ship started sailing S 42°35’ W at the rate of 5 kph. After 2 hours, ship B started at the same port going N 46°20’ W at the rate of 7 kph. After how many hours will the second ship be exactly north
4.03
8 - A spherical triangle ABC has an angle C = 90° and sides a = 50° and c = 80°. Find the value of b in degrees.
74.33
9 - A wire supporting a pole is fastened to it 20 feet from the ground and to the ground 15 feet from the pole. Determine the length of the wire and the angle it makes with the pole.
25 ft, 36.87°
10 - An aero lift airplane can fly at airspeed of 300 mph. If there is a wind blowing towards the cast at 50 mph, what should be the plane’s compass heading in order for its course to be 30°? What will be
21.7°, 321.8 mph
11 - Arc tan [2 cos (arc sin [(3^(1/2))/2]) / 2]) is equal to
Ï€/4
12 - By expressing cos 113° in terms of trigonometrical ratios, answer will be
− cos 67° = -0.3907
13 - By expressing cos 82° in terms of trigonometrical ratios, answer will be
− cos 98° = -0.1392
14 - By expressing sin 125° in terms of trigonometrical ratios, answer will be
sin 55° = 0.8192
15 - By expressing sin 170° in terms of trigonometrical ratios, answer will be
sin 10° = 0.1736
16 - Considering 0° < x < 180°, angle of cos x = -0.8726 is
150.76°
17 - Considering 0° < x < 180°, angle of sin x = 0.2385 is
13.80° , 166.20°
18 - Considering Cosine Rule of any triangle ABC, possible measures of angle A includes
all of above
19 - Considering Cosine rule, a² + c² - b²⁄2ac is equal to
cos B
20 - Considering Cosine rule, b² + c² - a²⁄2bc is equal to
cos A
21 - Considering Cosine rule, cos C is equal to
a² + b² - c²⁄2ab
22 - Cos²2θ =
1 + sin²Î¸
23 - Cosine Rule is also known as
Cosine Formula
24 - Csc 520° is equal to:
csc 20°
25 - Csc²Î¸/2-cot²Î¸/2 =
-1
26 - Determine the spherical excess of the spherical triangle ABC given a = 56°, b = 65°, and c = 78°.
68°37’
27 - Determine the value of the angle of an isosceles spherical triangle ABC whose given parts are b = c = 54°28’ and a = 92°30’.
89°45’
28 - Dimensions of plane includes
breadth and length
29 - Dimensions of solid includes
height
30 - Evaluate arc cot [2cos (arc sin 0.5)]
30°
31 - Evaluate: (2sinθcosθ-cosθ)/(1 – sin θ+ sin^2θ – cos^2θ)
cot θ
32 - Find the value of (sin θ + cos θ tanθ)/cos θ
2 tan θ
33 - Find the value of A between 270° and 360° if sin^2 A – sin A = 1
330°
34 - Find the value of sin (arc cos15/17)
45155
35 - Find the value of y in the given: y = (1 + cos θ) tan θ
sin 2θ
36 - Flat surface like blackboard is classified as
plane
37 - For any acute angle, cosine A is equal to
-cos (180° - A)
38 - For any acute angle, sine A is equal to
sin (180° - A)
39 - For Cosine Rule of any triangle ABC, a² is equal to
b² + c² - 2bc cos A
40 - For Cosine Rule of any triangle ABC, b² is equal to
a² + c² - 2ac cos B
41 - For Cosine Rule of any triangle ABC, c² is equal to
a² + b² - 2ab cos C
42 - Formula for area of a triangle ABC is
1/2ab sin C = 1/2bc sin A = 1/2ac sin B
43 - Given a right spherical triangle whose parts are a = 82°, b = 62°, and C = 90°. What is the value of the side opposite the right angle?
86°15’
44 - If an equivalent triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle.
34.64 cm
45 - If conversed sin θ= 0.134, find the value of θ
60°
46 - If cos 55° and sin 55° = 0.8 each then answer of 3 cos 125° + 5 sin 125° is
1.6
47 - If cos 55° and sin 55° = 0.8 each then answer of cos 125° + 5 sin 55° is
2.4
48 - If cos 65° + cos 55° = cos θ, find θ in radians
0.087
49 - If cosine is 0.8 then value of acute angle is
36.87°
50 - If Greenwich Mean Time (GMT) is 6 A.M, what is the time at a place located 30° East longitude?
8 A.M.
51 - If sec 2A =1/sin13A, determine the angle A in degrees.
6°
52 - If sin 3A = cos 6B, the
A + 2B = 30°
53 - If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.39x, find the value of x?
0.256
54 - If sin x cos x + sin 2x = 1, what are the values of x?
20.90°, 69.1°
55 - If sine is 0.2586 then value of acute angle is
14.99°
56 - If tan x =1/2, tan y = 1/3, what is the value of tan (x + y)?
1
57 - If the longitude of Tokyo is 139°E and that of Manila is 121°E, what is the time difference between Tokyo and Manila?
1 hour and 10 minutes
58 - In a triangle ABC, if angle A = 72° , angle B = 48° and c = 9 cm then Ĉ is
66°
59 - Line which is perpendicular to line passing through intersection point is called
normal
60 - Number of dimensions a line can have is
one
61 - Number of dimensions a point can have is
negative
62 - One degree on the equator of the earth is equivalent to _____ in time.
1 hour
63 - Points A and B 1000 m apart are plotted on a straight highway running East and West. From A, the bearing of a tower C is 32° W of N and from B the bearing of C is 26° N of E. Approximate the shortest
374 m
64 - Sec²Î¸-tan²Î¸ =
0
65 - Simplify the equation sin^2θ(1 + cot^2θ)
1
66 - Simplify the following: [(cos A + cos B)/(sin A – sin B)] + [(sin A + sin B)/(cos A – cos B)]
0
67 - Sine rule for a triangle states that
sin A/a = sin B/b = sin C/c
68 - Solve for A for the given equation cos 2A = 1 – cos 2A
45, 135, 225, 315 degrees
69 - Solve for angle C of the oblique spherical triangle ABC given, a = 80°, c = 115° and A = 72°
95°
70 - Solve for G if csc (11G – 16 degrees) = sec (5G + 26 degrees)
5 degrees
71 - Solve for side b of a right spherical triangle ABC whose parts are a = 46°, c = 75° and C = 90°.
48°
72 - Solve for the value of A° when sin A = 3.5 x and cos A = 5.5 x
32.47°
73 - Solve for the θ in the following equation: Sin 2θ = cos θ
30°
74 - Solve for x in the equation: arc tan (x + 1) + arc tan (x – 1) = arc tan (12)
1.34
75 - Solve for x in the given equation: Arc tan (2x) + arc tan (x) = π/4
0.281
76 - Solve for x, if tan 3x = 5 tan x
20.705°
77 - Solve the angle A in the spherical triangle ABC given a = 106°25’, c = 42°16’ and B = 114°53’
45°54’
78 - Solve the remaining side of the spherical triangle whose given parts are A = B = 80° and a = b = 89°.
168°31’
79 - The sides of a triangle are 195, 157 and 210, respectively. What is the area of the triangle?
14,586 sq. units
80 - The sides of a triangle are 8, 15, and 17 units. If each side is doubled, how many square units will the are of the new triangle be?
240
81 - The sides of a triangular lot are 130 m, 180 m and 190 m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. Find the length of the line
125 m
82 - The sine of a certain angle is 0.6, calculate the cotangent of the angle.
45019
83 - The two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26°. What is the third side?
341.78 m
84 - Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other triangle is 3 units less than its base. Find the altitudes, if the areas of the
4 and 10
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