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.
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..
2 answers
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
1 answer