Question

Given right triangle ABC, where angle m ‹A is equal to 45 °, m‹ B = 45°, m‹C=90° solve

3. a=_____________ b=8√3 c=________

4. a=________ b=__________ c=4​

Answer 1

A ) a = 8
`√(3)` , c = 8
`√(6)`

B ) a = 2
`√(2)` , b = 2
`√(2)`

Explanation:

Given as :

A ) ABC is right triangle , right angle at c

So, ∠ C = 90°

And ∠ A = 45° , ∠ B = 45°

And BC = a , CA = b , AB = c

measure of side b = 8
`√(3)`

Now, from right angle triangle ABC

Tan ∠ C =
`(\textrm Perpendicular)/(\textrm Base)`

Or, Tan 45° =
`(\textrm a)/(\textrm b)`

or, 1 =
}[/tex]

∴ a = 8
`√(3)`

Now, c² = a² + b²

Or, c² = ( 8
`√(3)` )² + (8
`√(3)` )²

Or, c = 8
`√(6)`

Again

B ) c = 4

So, Sin ∠ A =
`(\textrm Perpendicular)/(\textrm Hypotenuse)`

or , Sin 45° =
`(\textrm a)/(\textrm 4)`

Or , a = 4 × Sin 45°

∴ a = 4 ×
`(1)/(√(2) )`

I.e a = 2
`√(2)`

Now , b² = c² - a²

Or, b² = 4² - (2
`√(2)`)²

Or, b² = 16 - 8 = 8

Or , b = 2
`√(2)`

Hence the solution of given expression

A ) a = 8
`√(3)` , c = 8
`√(6)`

B ) a = 2
`√(2)` , b = 2
`√(2)` Answer