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In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=17°, and RS = 84 feet. Find the length of QR to the nearest tenth of a foot.



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Respuesta :

SaniShahbaz

Answer:

The length of QR to the nearest tenth of a foot is 287.28 feet.

Step-by-step explanation:

Let a right angled Triangle QRS have base SQ, perpendicular RS and Hypotenuse QR.

∠S = 90°

∠Q = 17°

Perpendicular = 84 ft

We know that for a right angle triangle

SinΘ = perpendicular/Hypotenuse

Sin ∠Q = 84/QR

QR = 84/sin(17°)

QR = 84/0.2924

QR = 287.2777

QR = 287.28 feet

aksnkj

Use the concept of trigonometric ratios in ΔQRS. The length of QR to the nearest tenth of a foot will be 287.7.

Given,

Angle S of triangle QRS is of 90 degrees and Angle Q is 17 degrees.

The length of side RS is 84 feet.

Since the angle S is 90 degree so the triangle QRS is a right triangle.

So the side QR will be its hypotenuse.

How to find trigonometric ratios?

Now by Applying trigonometric ratios in [tex]\Delta QRS[/tex], we get

[tex]\rm sin17^\circ=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]0.292=\dfrac{84}{\rm QR}[/tex]

[tex]\rm QR =\dfrac{84}{0.292}[/tex]

[tex]\rm QR=287.67[/tex]

Hence the length of QR to the nearest tenth of a foot is 287.7 .

For more details on Trigonometric ratios follow the link:

https://brainly.com/question/1201366

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