\fdO'^ - Old Forge Coal Mines

1G4 GEOMETRY AND TRIGONOMETRY.
(354) In the triangle
ABC, Fijr. 19,
AB=24: feet,
BC= 11.25 feet, and
AC^ 18 feet.
— tt,
m-\-n : a-\-b:'.a — m
m
b :
or 24 : 29.25 :: 6.75 :
29.25 X 6.75 _
m — n= — = 8.226562. oofiKco
24
Adding in + n and m—n, we have
w 4- « = 24
;;/ - ;/ = 8.226562
2 w/ = 32.226562
m- 16.113281.
Subtracting m — n from m -\- «, we have
— n
2« = 15.773438
n= 7.886719.
In the triangle ADC, side AC=\^ feet, side AD =
16.113281; hence, according to Rule 3, Art. 754, cos A =
IB 1 1 "i^RI
7_ = .89518, or angle A = 26° 28' 5'. In the triangle
18
B D C, side B D = 7.SS6719, and side BC= 11.25 ft.
Hence, cos B = "^ff^JJ^ = . 70104, or angle B = 45° 29' 23'.
11. 2o
Angle C = 180° - (45° 29' 23' + 26° 28' 5') = 108° 2' 32*.
A = 26° 28' 5'.
Ans. ^ B = A5° 29' 23'.
C = 108° 2' 32'.