Answer:
x = 25
y=16.3
z=73.7
Step-by-step explanation:
Given :
[tex]AC=x\,,\,AB= 7 \,\,in.\,,\,BC=24\,\,in.[/tex]
[tex]\angle A=z\,,\,\angle C=y[/tex]
To find : x, y and z
Solution:
Pythagoras theorem:
In right angled triangle, square of hypotenuse is equal to sum of squares of the remaining two sides .
Here, [tex]\Delta ABC[/tex] is right angled at B
On applying pythagoras theorem, we get
[tex]AC^2=AB^2+BC^2\\x^2=24^2+7^2\\x^2=576+49\\x^2=625\\x=25[/tex]
Also, we know that [tex]\tan \theta[/tex] = perpendicular/ Base
[tex]\tan A=\tan z=\frac{BC}{AB}=\frac{24}{7}\\\\\Rightarrow z=\arctan \left ( \frac{24}{7} \right )=73.7[/tex]
[tex]\tan C=\tan y=\frac{AB}{BC}=\frac{7}{24}\\\\\Rightarrow y=\arctan \left ( \frac{7}{24} \right )=16.3[/tex]
