Question

question
solve for ( x ). round to the nearest tenth, if necessary.
triangle with right angle at h, angle at i is 26 degrees, side gh is 6.5, side ih is ( x )
answer
attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle $\triangle IHG$, right-angled at $H$. For $\angle I = 26^\circ$, side $GH = 6.5$ is the opposite side, and side $IG = x$ is the hypotenuse. We use the sine ratio: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(26^\circ) = \frac{6.5}{x}$

Step2: Rearrange to solve for $x$

Rearrange the equation to isolate $x$:
$x = \frac{6.5}{\sin(26^\circ)}$

Step3: Calculate the value

First, find $\sin(26^\circ) \approx 0.4384$. Substitute this value:
$x \approx \frac{6.5}{0.4384} \approx 14.8$

Answer:

$x = 14.8$