Question

1-4 Determine the value of the following5. Find m

Answer 1

Answers:

1) $cos B=\frac{4}{5}=0.8$

2) $csc A=\frac{5}{3}=1.66$

3) $sec B=\frac{5}{4}=1.25$

4) $tan A=\frac{3}{4}=0.75$

5) $z=38.65\°$

Step-by-step 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) $cos B=\frac{Adjacent-side}{hypotenuse}$

$cos B=\frac{4}{5}=0.8$

2) $csc A=\frac{1}{sin A}$

$\frac{1}{sin A}=\frac{1}{\frac{5}{3}}$

Then:

$csc A=\frac{5}{3}=1.66$

3) $sec B=\frac{1}{cos B}$

$frac{1}{cos B}=\frac{1}{\frac{4}{5}}$

Then:

$sec B=\frac{5}{4}=1.25$

4) $tan A=\frac{opposite-side}{adjacent-side}=\frac{3}{4}$

Then:

$tan A=\frac{3}{4}=0.75$

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:

$tan z=\frac{opposite-side}{adjacent-side}$

$tan z=\frac{8}{10}$

Finding the value of $z$:

$z=tan^{-1}\frac{8}{10}$

$z=38.65\°$