Full resolution (JPEG) - On this page / på denna sida - Geometry - Solution of right angle triangles
<< prev. page << föreg. sida << >> nästa sida >> next page >>
Below is the raw OCR text
from the above scanned image.
Do you see an error? Proofread the page now!
Här nedan syns maskintolkade texten från faksimilbilden ovan.
Ser du något fel? Korrekturläs sidan nu!
This page has never been proofread. / Denna sida har aldrig korrekturlästs.
TRIGONOMETRY. 1 77
Fig. 1 9
^ ^1 f
Example.
Find angles a and b and the
side X in the right-angled triangle.
(Fig. 19).
*~ 12.5 feet *
Tangent corresponding to a = 125 = 0.4
12.5
Tangent corresponding to b = —^— = 2.5
By the trigonometrical table the angles are obtained thus
:
Tangent 0.40000 gives 21° 48’
Tangent 2.50000 gives 68° 12’
Therefore
:
Angle a = 21° 48’ and angle b = 68° 12’.
Angle b may also be found by subtracting angle a from
90c
, thus
:
Angle b = 90° — 21° 48’ = 68° 12’
The length of the side X may be found thus
:
5
x sin. c
5
* — 0.37137
x — 13.464 feet long.
By means of logarithms the length of the side x is obtained
thus
:
Log. x = log. 5 — log. sin. 21° 48’
Log. x = 0.698970 — (9.569804 — 10)
Log. x = 1.129166
x — 13.464 feet long.
Note.—In a right-angle triangle (see Fig. 18) the side A is
called the perpendicular, B the base and C the hypothenuse.
Hence, divide the perpendicular by the hypothenuse and the
quotient is the sine of the angle between the base and the
hypothenuse. Divide the base by the hypothenuse and the
quotient is the cosine of the angle between the base and the
hypothenuse. Divide the perpendicular by base and the quo-
tient is the tangent of the angle between the base and the
hypothenuse. Divide the base by the perpendicular and the
quotient is the cotangent of angle between the base and the
hypothenuse.
<< prev. page << föreg. sida << >> nästa sida >> next page >>
