Question

solve for x. round to the nearest tenth, if necessary. triangle with right angle at t, ut = 75, angle at s is 26 degrees, side us is x

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right triangle (∠T = 90°). We know side UT = 75 (opposite to angle S = 26°) and we need to find hypotenuse x. The sine ratio is \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(26^\circ)=\frac{75}{x}\).

Step2: Solve for x

Rearrange the formula: \(x = \frac{75}{\sin(26^\circ)}\). Calculate \(\sin(26^\circ)\approx0.4384\). Then \(x=\frac{75}{0.4384}\approx171.1\).

Answer:

171.1