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In ΔSTU, the measure of ∠U=90°, the measure of ∠T=47°, and ST = 7.2 feet. Find the length of US to the nearest tenth of a foot.​

Respuesta :

calculista

Answer:

[tex]US=5.3\ ft[/tex]

Step-by-step explanation:

we know that

In the right triangle STU

The sine of angle T is equal to the opposite side angle T divided by the hypotenuse

[tex]sin(T)=\frac{US}{ST}[/tex]

substitute the values

[tex]sin(47\°)=\frac{US}{7.2}[/tex]

[tex]US=(7.2)sin(47\°)=5.3\ ft[/tex]

akposevictor

Applying the trigonometry ratio, SOH, the length of US is: 5.3 feet

Recall the Trigonometry Ratio, SOH:

SOH stands for: sin ∅ = Opposite/hypotenuse

Given the following for ΔSTU:

  • m∠U = 90°
  • m∠T = 47°
  • Side ST = 7.2 feet.

Therefore, applying the trigonometry ratio, SOH, we have the following:

Reference angle (∅) = 47°

US = opposite = ?

ST = hypotenuse = 7.2 feet

  • Plug in the  values:

sin 47° = US/7.2

US = (sin 47°)(7.2)

US = 5.3 feet

Learn more about trigonometry ratio on:

https://brainly.com/question/4326804

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