Question

1-4 Determine the value of the following

5. Find m

Answer 1

Answers:

1)
`cos B=(4)/(5)=0.8`

2)
`csc A=(5)/(3)=1.66`

3)
`sec B=(5)/(4)=1.25`

4)
`tan A=(3)/(4)=0.75`

5)
`z=38.65\°`

Explanation:

First exercise:

We have a right triangle with the values of each side an we have to find the following trigonometic functions (taking into account the secant function
`sec` is the inverse of the cosine, the cosecant
`csc` is the inverse of the sine):

1)
`cos B=(Adjacent-side)/(hypotenuse)`

`cos B=(4)/(5)=0.8`

2)
`csc A=(1)/(sin A)`

`(1)/(sin A)=(1)/((5)/(3))`

Then:

`csc A=(5)/(3)=1.66`

3)
`sec B=(1)/(cos B)`

`frac{1}{cos B}=(1)/((4)/(5))`

Then:

`sec B=(5)/(4)=1.25`

4)
`tan A=(opposite-side)/(adjacent-side)=(3)/(4)`

Then:

`tan A=(3)/(4)=0.75`

Second exercise:

5) Here, we are given another right triangle and we have to find the measure of the angle
`z`.

So, according to the figure, we can use the tangent function:

`tan z=(opposite-side)/(adjacent-side)`

`tan z=(8)/(10)`

Finding the value of
`z`:

`z=tan^(-1)(8)/(10)`

`z=38.65\°`