Respuesta :

mhanifa

Answer:

  • t = 6

Step-by-step explanation:

Given ΔRST with:

  • sin ∠T = 1/5
  • m ∠R = 30°
  • r = 15
  • t = ?

Solution

We know t is opposite ∠T and r is opposite ∠R.

Use the law of sines to find the missing value of t.

  • r / sin ∠R = t / sin ∠T

Substitute the known values and solve for t:

  • 15 / sin (30°) = t / (1/5)
  • 15 / (1/2) = 5t
  • 30 = 5t
  • t = 30/5
  • t = 6
semsee45

Answer:

t = 6

Step-by-step explanation:

In ΔRST:

  • Angle R is opposite side r.
  • Angle S is opposite side s.
  • Angle T is opposite side t.

Sine Rule

[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Given:

  • sin T = ¹/₅
  • R = 30°
  • r = 15

Substitute the given values into the Sine Rule formula and solve for t:

[tex]\implies \sf \dfrac{r}{\sin R}=\dfrac{s}{\sin S}=\dfrac{t}{\sin T}[/tex]

[tex]\implies \sf \dfrac{15}{\sin 30^{\circ}}=\dfrac{t}{\frac{1}{5}}[/tex]

[tex]\implies \sf \dfrac{15}{\sin 30^{\circ}}=5t[/tex]

[tex]\implies \sf t=\dfrac{15}{5 \sin 30^{\circ}}[/tex]

[tex]\implies \sf t=\dfrac{15}{5 \cdot \frac{1}{2}}[/tex]

[tex]\implies \sf t=\dfrac{15}{\frac{5}{2}}[/tex]

[tex]\implies \sf t=15 \cdot \dfrac{2}{5}[/tex]

[tex]\implies \sf t=\dfrac{30}{5}[/tex]

[tex]\implies \sf t=6[/tex]

Learn more about the Sine Rule here:

https://brainly.com/question/27089170

https://brainly.com/question/28033514

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