The correct ratios are: cse 27=23/RT, sec 27= 23/10.4 and cot 63 = RT/10.4
In triangle RST, angle T= 90° and angle R= 63°
As the total of all angle in any triangle is 180°, so the measure of the angle S = 180°- (90°+63°)
S= 180°- 153°
S= 27°
According to the rule of trigonometric ratios,
[tex] cse(\theta) = \frac{hypotenuse}{opoosite}\\ \\ sec(\theta)=\frac{hypotenuse}{adjacent} \\ \\ cot(\theta)= \frac{adjacent}{opposite} [/tex]
In respect of angle R (63°), side RS(23) is hypotenuse , ST(10.4) is opposite and RT is adjacent.
So, cse(63°) =[tex] \frac{23}{10.4} [/tex]
sec(63°) = [tex] \frac{23}{RT} [/tex]
cot(63°) = [tex] \frac{RT}{10.4} [/tex]
Now, in respect of angle S(27°), hypotenuse is RS(23), adjacent is ST(10.4) and opposite is RT.
So, cse(27°) = [tex] \frac{23}{RT} [/tex]
sec(27°) = [tex] \frac{23}{10.4} [/tex]
cot(27°) = [tex] \frac{10.4}{RT} [/tex]
