Question

Find x. Round to the nearest tenth: 29 500 ft

Answer 1

Answer:

437.3ft

Step-by-step explanation:

last of sines

a/sin(A) = b/sin(B) = c/sin(C)

sin(90) = 1

the angle between y and 500ft side is 90-29 = 61 degrees.

so,

x/sin(61) = 500/1 = 500

x = 500 × sin(61) = 437.3ft

Answer 2

In a triangle, value of $x = 437.4$ units (round to nearest tenth) using trigonometric ratio.

What is trigonometric ratio?

"Trigonometric ratio is defined as in a right triangle the relation between the ratio of a sides of a triangle and the angle."

Formula used

$sin\theta = \frac{opposite sides}{hypotenuse}$

$cos\theta = \frac{adjacent sides}{hypotenuse}$

According to the question,

In a given right triangle ABC,

Hypotenuse $=500 ft$

Opposite side $= x ft$

Adjacent side $= y ft$

As per the diagram drawn,

 $\angle BAC+ 29\° = 90\° \\\\\implies \angle BAC = 90\° -29\° \\\\\implies \angle BAC = 61\°$

Substitute the value in the above trigonometric ratio formula we get,

$sin61\° = \frac{x}{500}\\\\\implies 0.8747 = \frac{x}{500}\\\\\implies x = 500 \ times 0.8747\\\\\implies x = 437.35 ft$

$\implies x = 435.4 ft$ (round to nearest tenth)

In trigonometric ratio $cos\theta$ we get,

$cos61\° = \frac{y}{500}\\\\\implies 0.4848 = \frac{y}{500}\\\\\implies y= 500 \ times 0.4848\\\\\implies y = 242.2 ft$

Hence , In a triangle, value of $x = 437.4$ units (round to nearest tenth) using trigonometric ratio.

Learn more about trigonometric ratio here,

https://brainly.com/question/1201366

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