Question

solve for x. round to the nearest tenth, if necessary.

answer attempt 1 out of 2
x =

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle IHG \) (right - angled at \( H \)), we know that \( \angle I = 26^{\circ} \), the side opposite to \( \angle I \) is \( HG = 6.5 \) and the hypotenuse is \( IG=x \). The sine of an angle in a right triangle is defined as \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(26^{\circ})=\frac{HG}{IG}=\frac{6.5}{x} \).

Step2: Solve for \( x \)

From \( \sin(26^{\circ})=\frac{6.5}{x} \), we can re - arrange the formula to solve for \( x \). Cross - multiplying gives us \( x=\frac{6.5}{\sin(26^{\circ})} \).
We know that \( \sin(26^{\circ})\approx0.4384 \). Then \( x = \frac{6.5}{0.4384}\approx14.8 \) (rounded to the nearest tenth).

Answer:

\( x\approx14.8 \)