Question

Right △ABC has its right angle at C, BC=4 , and AC=8 .

What is the value of the trigonometric ratio?

Drag a value to each box to match the trigonometric ratio.

Answer 1

Therefore,

`cos A=(2√(5))/(5)`

`\cot B =(1)/(2)`

`\csc B = (√(5))/(2)`

Explanation:

Given:

Right △ABC has its right angle at C,

BC=4 , and AC=8 .

To Find:

Cos A = ?

Cot B = ?

Csc B = ?

Solution:

Right △ABC has its right angle at C, Then by Pythagoras theorem we have

`(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)`

Substituting the values we get

`(AB)^(2)=4^(2)+8^(2)=80\\AB=√(80)\\AB=4√(5)`

Now by Cosine identity

`\cos A = \frac{\textrm{side adjacent to angle A}}{Hypotenuse}\\`

Substituting the values we get

`\cos A = (AC)/(AB)=(8)/(4√(5))=(2)/(√(5))\\\\Ratinalizing\\\cos A=(2√(5))/(5)`

`cos A=(2√(5))/(5)`

Now by Cot identity

`\cot B = \frac{\textrm{side adjacent to angle B}}{\textrm{side opposite to angle B}}`

Substituting the values we get

`\cot B = (BC)/(AC)=(4)/(8)=(1)/(2)`

Now by Cosec identity

`\csc B = \frac{Hypotenuse}{\textrm{side opposite to angle B}}\\`

Substituting the values we get

`\csc B = (AB)/(AC)=(4√(5))/(8)=(√(5))/(2)`

Therefore,

`cos A=(2√(5))/(5)`

`\cot B =(1)/(2)`

`\csc B = (√(5))/(2)`