Asked by AlphaPrimes
Triangle HAV has <H = 124, a=8.5mm, and h=7.2mm
How many solutions are there?
What I attempted:
SinH/h=SinA/a
Sin124/7.2=SinA/8.5
SinA=8.5(Sin124/7.2)
<A = 78.2
RULE => All interior angles must add up to 180 degrees therefore this triangle has 0 solutions.
The textbook says that there are two solutions though..
How many solutions are there?
What I attempted:
SinH/h=SinA/a
Sin124/7.2=SinA/8.5
SinA=8.5(Sin124/7.2)
<A = 78.2
RULE => All interior angles must add up to 180 degrees therefore this triangle has 0 solutions.
The textbook says that there are two solutions though..
Answers
Answered by
Steve
Your math is correct. The text is wrong.
If one angle is obtuse, there can be only one solution. Or none, if the conditions preclude it, as in this case.
I suspect a typo in the problem.
If one angle is obtuse, there can be only one solution. Or none, if the conditions preclude it, as in this case.
I suspect a typo in the problem.
Answered by
Reiny
I got the same result, so I am with you.
No solution.
I verified the "no solution" by using the cosine law to find HA
let HA = x
then :
7.2^2 = x^2 + 8.5^2 - 2x(8.5)cos124°
x^2 + 9.506x + 20.41 = 0
x = -3.276 or x = -6.23
but x can't be negative, confirming our conclusion that there is no solution
Either the textbook is wrong or there was an error in stating the problem.
It is not possible to "construct" a triangle with the given data
No solution.
I verified the "no solution" by using the cosine law to find HA
let HA = x
then :
7.2^2 = x^2 + 8.5^2 - 2x(8.5)cos124°
x^2 + 9.506x + 20.41 = 0
x = -3.276 or x = -6.23
but x can't be negative, confirming our conclusion that there is no solution
Either the textbook is wrong or there was an error in stating the problem.
It is not possible to "construct" a triangle with the given data
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