Answer:
The expressions that show the value of q are
1) [tex]q=\sqrt{r^{2}+s^{2}}[/tex]
2) [tex]q=\frac{s}{cos(55\°)}[/tex]
3) [tex]q=\frac{r}{sin(55\°)}[/tex]
4) [tex]q=\frac{s}{sin(35\°)}[/tex]
5) [tex]q=\frac{r}{cos(35\°)}[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
case A)
In the right triangle of the figure
Applying the Pythagoras Theorem
[tex]q^{2}=r^{2}+s^{2}[/tex]
[tex]q=\sqrt{r^{2}+s^{2}}[/tex]
case B)
In the right triangle of the figure
[tex]cos(55\°)=\frac{s}{q}[/tex]
solve for q
[tex]q=\frac{s}{cos(55\°)}[/tex]
case C)
In the right triangle of the figure
[tex]sin(55\°)=\frac{r}{q}[/tex]
solve for q
[tex]q=\frac{r}{sin(55\°)}[/tex]
case D)
In a right triangle
if [tex]A+B=90\°[/tex]
then
[tex]cos(A)=sin(B)[/tex]
therefore
[tex]q=\frac{s}{cos(55\°)}[/tex]------> [tex]q=\frac{s}{sin(35\°)}[/tex]
[tex]q=\frac{r}{sin(55\°)}[/tex] ------> [tex]q=\frac{r}{cos(35\°)}[/tex]
The expression that shows the value of q is q = √r² + s²
Right triangle has one of its angle as 90 degrees. The sides can be found using Pythagoras theorem.
Therefore,
where
c = hypotenuse
a and b are the other legs.
The hypotenuse is the longest side of a right angle triangle.
Therefore,
s = adjacent side
r = opposite side
q = hypotenuse
Therefore,
q² = r² + s²
square root both sides
q = √r² + s²
learn more on right triangle here: https://brainly.com/question/1092242
