Question

In triangle r s t, angle r = 63 degrees, angle t = 90 degrees, side r s = 23 and side s t = 10.4. which ratios are correct?

Answer 1

The correct ratios are: cos 27=23/RT, sec 27= 23/10.4 and cot 63 = RT/10.4

What is trigonometry  ratio in tringle?

• Trigonometric ratios are the ratios of the length of sides of a triangle.
• These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.
• The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

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,

cos(θ) = $\frac{hypotenuse}{opposite}$

sec(θ) = $\frac{hypotenuse}{adjacent}$

cot(θ) = $\frac{adjacent}{opposite}$

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

cos(63°) = $\frac{23}{10.4}$

sec(63°) = $\frac{23}{RT}$

cot(63°) = $\frac{RT}{10.4}$

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

So, cos(27°) = $\frac{23}{RT}$

sec(27°) = $\frac{23}{10.4}$

cot(27°) = $\frac{10.4}{RT}$

Learn more about trigonometry ratio

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