Question

Find the missing side lengths. Leave your answers as radicals in simplest form

Answer 1

a) Sin X = O/H

Sin 45 =
`7√(2)`/2/H

H=
`7√(2)`/2/ Sin 45

m= 7

b) cos X = A/H

cos 45= A/7

A= cos45*7

n= 4.95

Answer 2

Explanation:

Hi Mia, are you aware that the last name Hamilton is a famous math person? :) anyway,

The triangle in the picture is an isosceles triangle, we know that b/c the angle of the one is 45° meaning the other side must also be a 45° angle. So we know the two sides are the same length.

side n = 7
`√(2)` / 2

then use Pythagoras to find m

`c^(2)` = ( 7
`√(2)` / 2)^2 + ( 7
`√(2)` / 2)^2

`c^(2)` = 49*2/4 + 49*2/4

`c^(2)` = 49/2 + 49/2

`c^(2)` = 98/2

`c^(2)` = 49

c = 7

side m = 7 :) nice, huh ?