Question

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

What is the value of the trigonometric ratio?



sin A=



tan B=



sec A=

Answer 1

Part A)
`sin(A)=(√(5))/(5)`

Part B)
`tan(B)=2`

Part C)
`sec(A)=(√(5))/(2)`

Explanation:

see the attached figure to better understand the problem

step 1

Find the length side AB (hypotenuse of the right triangle)

Applying the Pythagorean Theorem

`AB^2=BC^2+AC^2`

substitute the given values

`AB^2=4^2+8^2`

`AB^2=80`

`AB=√(80)\ units`

simplify

`AB=4√(5)\ units`

step 2

Find sin(A)

we know that

In the right triangle ABC

`sin(A)=(BC)/(AB)` ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

`sin(A)=(4)/(4√(5))=(√(5))/(5)`

step 3

Find tan(B)

we know that

`tan(B)=(AC)/(BC)` ----> by TOA (opposite side divided by adjacent side)

substitute the values

`tan(B)=(8)/(4)=2`

step 4

Find sec(A)

we know that

`sec(A)=(1)/(cos(A))`

`cos(A)=(AC)/(AB)` ----> by CAH

so

`sec(A)=(AB)/(AC)`

substitute the values

`sec(A)=(4√(5))/(8)`

simplify

`sec(A)=(√(5))/(2)`