Answer:
see the procedure
Step-by-step explanation:
see the attached figure to better understand the problem
we will analyze two cases
Part 1)
First case
The angle x is the angle C
so
In the right triangle ABC
[tex]sin(C)=\frac{AB}{AC}[/tex] ---> by SOH (opposite side divided by the hypotenuse)
substitute the given values
[tex]sin(C)=\frac{24}{26}[/tex]
using a calculator
[tex]C=sin^{-1}(\frac{24}{26})=67^o[/tex]
therefore
The measure of angle x is 67 degrees
Part 2)
Second case
The angle x is the angle A
so
In the right triangle ABC
[tex]sin(A)=\frac{BC}{AC}[/tex] ---> by SOH (opposite side divided by the hypotenuse)
substitute the given values
[tex]sin(A)=\frac{10}{26}[/tex]
using a calculator
[tex]A=sin^{-1}(\frac{10}{26})=23^o[/tex]
therefore
The measure of angle x is 23 degrees
