In triangle ABC, AB =8, AC=6 and angle ABC =25 find BAC. Explain the workings
2006-09-22 01:39:14 · 7 answers · asked by edwinvandesar 1 in Science & Mathematics ➔ Mathematics
okay this is the updated version of question.
O, P and Q are 3 points on ground level. THe bearing of O from P is 30 degrees and the bearing of Q from O is 80 degrees. At O, there stands a tower, such that the angle of evlevation of the top of the tower is 50 degrees from Q and 20 degrees from P. The distance PQ =150. Find the height of the tower.
This is NOT A HOMEWORK QUESTION but a self practice one inpreparation for exam
2006-09-22 18:48:41 · update #1
Let AD be the line dropped from A which is perpendicular to BC
(therefore, you have 2 right triangles)
Let AD = x
angle BAD + angle CAD = angle BAC
since we are looking for the value of angle BAC,
we must first find the value of x
sin 25 = x/8
multiply both sides by 8
8sin 25 = x
which will give you
x = 3.380946094
we now know the value of x so, we can now find the value of angle BAD
cos BAD = x/8
cos BAD = 3.380946094/8
cos^(-1) 3.380946094 = 65
therefore, angle BAD is 65 degrees.
to find the value of angle CAD,
cos CAD = 3.380946094/6
cos^(-1) 0.563491015 = 55.70242977
angle BAC = 65+55.70242977 = 120.7024298
therefore, angle BAC is 120.70 degrees
2006-09-22 02:06:07 · answer #1 · answered by dengshii_0515 2 · 0⤊ 0⤋
HOMEWORK!!!!
Find angle ACB by using the law of sines. You know the length AC (6) and the opposite angle (25 degrees). You also know the length opposite angle ACB (i.e. AB=8), so you can solve for the angle ACB. Then use the fact that the sum of all the angles is 180 degree and you can solve for BAC.
2006-09-22 08:48:48 · answer #2 · answered by mathematician 7 · 1⤊ 0⤋
Let AB= c= 8
AC = b = 6
BC= a
Angle ABC= Angle b = 25
Angle BCA= Angle c
Angle BAC= Angle a
Using Sin law
c/sin c =b/sin b
8/sin c = 6/ sin 25
sin c =(8* sin25)/6
angle c = sin^-1{(8* sin25)/6}=34.3 degrees
Since angle(A+B+C) =180
angle A = 180 - 25 - 34.3 = 120.7 degrees
2006-09-22 11:46:14 · answer #3 · answered by Amar Soni 7 · 0⤊ 0⤋
It is not 90. That would only work if the angle between the two sides of 6 and 8 was 90, and it is not. That law of squares only works for right triangles.
2006-09-22 09:02:23 · answer #4 · answered by JJ M 2 · 0⤊ 1⤋
90 answer
ac=10
under root of [8 square +6 squre ] = 10 =ac
bac= 25 is superficial data ; not to be used .
2006-09-22 08:55:31 · answer #5 · answered by deepak57 7 · 0⤊ 0⤋
1. Use sin law:
sen(25)/8m = sen (ABC)/6m
2. Again sin law or you can use cosin law.
2006-09-22 09:06:11 · answer #6 · answered by Juan D 3 · 0⤊ 0⤋
AC/sin(ABC)=AB/sin(ACB) => ACB=...
BAC=180-ABC-ACB
2006-09-22 08:50:48 · answer #7 · answered by The Greek Guy 3 · 0⤊ 0⤋