Question

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

Answer 1

C

Explanation:

Answer 2

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) =
`(hypotenuse)/(opposite)`

sec(θ) =
`(hypotenuse)/(adjacent )`

cot(θ) =
`(adjacent)/(opposite)`

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

So, cse(63°) =
`(23)/(10.4)`

sec(63°) =
`(23)/(RT)`

cot(63°) =
`(RT)/(10.4)`

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

So, cse(27°) =
`(23)/(RT)`

sec(27°) =
`(23)/(10.4)`

cot(27°) =
`(10.4)/(RT)`