Question

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

(image of a right triangle ghi with right angle at h, gh = 5.6, angle at i is 29 degrees, hypotenuse gi is x)

answer attempt 1 out of 2
x = blank box submit button partially visible

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( GHI \), \( \angle I = 29^\circ \), opposite side to \( \angle I \) is \( GH = 5.6 \), and hypotenuse is \( x \). We use sine function: \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So \( \sin(29^\circ)=\frac{5.6}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{5.6}{\sin(29^\circ)} \). Calculate \( \sin(29^\circ)\approx0.4848 \). Then \( x=\frac{5.6}{0.4848}\approx11.6 \).

Answer:

\( x \approx 11.6 \)