In triangle rst, angle r = 63 degrees, angle t=90 degrees, side rs =23, side st = 10.4. which ratios are correct. csc63=23/rt, sec 63=23/10.4, and cot 27=10.4/rtcsc63=23/rt, sec 27=10.4/23, and cot63=10.4/rtcsc63=23/rt, sec 27= 23/10.4, and cot 63 = rt/10.4csc63=23/rt, sec 63=10.4/23, and cot27=rt/10.4

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,

cse(θ) =

sec(θ) =

cot(θ) =

In respect of angle R (63°), side RS(23) is hypotenuse , ST(10.4) is opposite and RT is adjacent.

So, cse(63°) =

sec(63°) =

cot(63°) =

Now, in respect of angle S(27°), hypotenuse is RS(23), adjacent is ST(10.4) and opposite is RT.

So, cse(27°) =

sec(27°) =

cot(27°) =

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answer: about 22.67

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