Question

state if 3 side lengths form acute, obtuse, or right triangle.
(8km, 11km, √185km) and (√23mi , 11mi, 12mi) and (14 yd, 17yd, 14√2yd) and (7ft, 7ft, √149ft) Please help me I don't know what to do!

Answer 1

use pythagoras theorem



square all the side measurements

if thesum of the squares of the shorter sides is equal to the square of the longer side the triangle is right angled...

\[a^2 + b^2 = c^2\]


e.g. \[8^2 + 11^2 = (\sqrt{185})^2... or..... 64 + 121 = 185\]

so this triangle is right angled.

if \[ c^2 < a^2 + b^2\] the triangle is acute

if \[c^2 > a^2 + b^2 \] the triangle is obtuse.

hope this helps.

Answer 2

for the 2nd one

\[(\sqrt{23}^2 = 23.... 11^2 = 121.... 12^2 = 144\]

so

23 + 121 = 144 ... so right angled.

Answer 3

thank you for you help hopefully I will get the rest right lol