Question

How to find the theta with side lengths of a triangle

Answer 1

Explanation:

Hello, there!!!

I hope you mean the question is like the above problem in picture.

so, let's simply work with it.

here, we may use cosine rule,

so, according to cosine rule,

`{c}^(2) = {a}^(2) + {b}^(2) - 2ab.cosc`

so, just put value of formulae here,

we get;

5^2 = 3^2 + 4^2 - (2×3×4) . cos thita

or, 25 = 9 + 16 -24 cos thita.

or, 24 cos thita = 0

or, cos thita = 0/25

or, cos thita = 0

now, taking cos to right side we get,

`{cos}^( - 1 ) (0)`

now, after typing cos ^-1 (0) we get angle as 90°.

(note: in step {cos thita = 0} you couold directly write like; cos thita = cos 90°. and cos would be cancelled in it as cos 90°=0. but it is only applied in particular angle like 0°,30°,60°,..... which are identified or if you don't know you must use the method above using calculator and remember to put inverse {cos^-1}).

so, In this way we find angle.

I hope it helps....