solve for $x$. round to the nearest tenth of a degree, if necessary.

題目

解題步驟

Understand the question
solve for $x$. round to the nearest tenth of a degree, if necessary.
Explanation
Step1: Identify trigonometric ratio

In right triangle $EFG$, for angle $x^\circ$ at $E$:
Opposite side to $x$: $FG = 34$
Hypotenuse: $EG = 46$
Use sine ratio: $\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$
Expression: $\sin(x) = \frac{34}{46}$

Step2: Simplify the ratio

Reduce the fraction:
Expression: $\sin(x) = \frac{17}{23} \approx 0.7391$

Step3: Solve for $x$

Take inverse sine of both sides:
Expression: $x = \sin^{-1}(0.7391)$

Step4: Calculate and round

Compute the angle and round to nearest tenth:
Expression: $x \approx 47.6^\circ$
Final answer
$47.6^\circ$

答案

Explanation

Step1: Identify trigonometric ratio

In right triangle $EFG$, for angle $x^\circ$ at $E$:
Opposite side to $x$: $FG = 34$
Hypotenuse: $EG = 46$
Use sine ratio: $\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$
Expression: $\sin(x) = \frac{34}{46}$

Step2: Simplify the ratio

Reduce the fraction:
Expression: $\sin(x) = \frac{17}{23} \approx 0.7391$

Step3: Solve for $x$

Take inverse sine of both sides:
Expression: $x = \sin^{-1}(0.7391)$

Step4: Calculate and round

Compute the angle and round to nearest tenth:
Expression: $x \approx 47.6^\circ$

Answer

$47.6^\circ$

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Question Analysis

Subject mathematics

Sub Subject geometry

Education Level high school

Difficulty unspecified

Question Type with image, calculation

Multi Question No

Question Count 1

Analysis Status completed

Analyzed At 2026-02-09T20:11:50

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solve for $x$. round to the nearest tenth of a degree, if necessary.

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