## Plane and Spherical Trigonometry |

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### Common terms and phrases

absolute value acute angle altitude angle in Quadrant angle of depression angle of elevation azimuth celestial celestial sphere centre circle of latitude colog computed cos2 cos2a cosB cosc cosecant cosine cosp cosy cota cotangent denote due east earth's ecliptic equal equation equinoctial Example Exercise feet find the angles Find the area Find the distance Find the height Find the value Hence horizontal plane hour angle hypotenuse included angle isosceles Law of Sines Leaving latitude log esc logarithms longitude meridian miles moving radius Napier's Rules negative oblique observer obtain perpendicular pole positive ratios regular polygon right angle right ascension right spherical triangle right triangle secant ship sails sin(s sin2 sinb siny solution solve the triangle spherical triangle star subtended tan2 tana tangent three sides tower trigonometric functions Trigonometry unit circle vertical whence

### Popular passages

Page 47 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 62 - The area of a triangle is equal to half the product of two sides and the sine of the included angle.

Page 19 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°. Find the height of the hill.

Page 46 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.

Page 16 - Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area...

Page 134 - Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian of the observer and the vertical circle passing through the point; it may also be regarded as the arc of the horizon intercepted between those circles.

Page 90 - Ans. ty. 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a...

Page 87 - Memorial Hall tower is 190 feet. From its top the angles of depression of the corners of the Delta which lie on Cambridge St. are 57° 44' and 16° 59', and the angle subtended by the line joining these corners is 99° 30'.

Page 137 - ZM= zenith distance of star = z, PZM= azimuth of star = a, A very simple relation exists between the hour angle of the sun and the local (apparent) time of day. Since the hourly rate at which the sun appears to move from east to west is 15°, and it is Apparent noon when the sun is on the meridian of a place, it is evident that if hour angle = 0°, 15°, — 15°, etc., time of day is noon, 1 o'clock pM, 11 o'clock AM, etc. In general, if...

Page 132 - The vertical circle passing through the east and west points of the horizon is called the Prime Vertical; that passing through the north and south points coincides with the celestial meridian.