Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you solve the right triangle ABC given A = 61°, a = 17, b = 19?

2 Answers

Jun 8, 2015

**If ABC is a right triangle **
$color(white)("XXXX")$ with $A = 61^@$
$color(white)("XXXX")$ and $a = 17$
$color(white)("XXXX")$ and $b = 19$
It might (at first appear that 2 configurations are possible:
enter image source here

$/_ B = 90^@$ (since it is a right triangle)
$/_C = 29^@$ (since $/_A+/_B+/_C = 180^@$
and
$c = sqrt(19^2 - 17^2)$ (approximately $8.485$ )

Unfortunately
Attempting to use the Law of Sines to verify these results:
$color(white)("XXXX")$ $(sin A)/a = (sin B)/b = (sin C)/c$

we get
$color(white)("XXXX")$ $(sin A)/a = sin(61^@)/17 = 0.051448$
and
$color(white)("XXXX")$ $(sin B)/b = sin(90^@)/19 = 0.052362$
and
$color(white)("XXXX")$ $(sin C)/c = sin(29^@)/8.485= 0.057135$

Conclusion
The given values are not those of a right triangle!

Jun 8, 2015

No solution is possible with the given data.

Related questions

See all questions in Solving Right Triangles

Impact of this question

2216 views around the world

You can reuse this answer
Creative Commons License