Question

State if the triangle is acute obtuse or right

Answer 1

The triangle is obtuse.

Explanation:

Using the sine rule to determine the other angle:

`(sinA)/(a) =(sinB)/(b) \\(sin90)/(10) =(sinB)/(8) \\10sinB=8sin90\\sinB=(8)/(10) \\B=sin^(-1) ((8)/(10) )\\B=53.1301`

180 - 53.1301 - 90 = 36.8699

Using sine rule again to determine the unknown length:

`(sinA)/(a) =(sinB)/(b) \\(sin90)/(10) =(sin36.8699)/(b) \\10sin36.8699=bsin90\\b=6`