State if the triangle is acute obtuse or right

Question

asked Dec 18, 2024 126k views

1 Answer

Luksurious · Answer 1 · 2024-12-24T13:12:53+0000

Answer:

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:

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