Question

find m∠u.

(image of right triangle vut with right angle at t, ut = 1.5, vt = 2.8)

write your answer as an integer or as a decimal rounded to the nearest tenth.

m∠u =
°

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(VTU\), \(\angle T = 90^\circ\), \(VT = 2.8\) (opposite to \(\angle U\)), \(UT = 1.5\) (adjacent to \(\angle U\)). We use the tangent function: \(\tan(\angle U)=\frac{\text{opposite}}{\text{adjacent}}=\frac{VT}{UT}\).

Step2: Calculate \(\tan(\angle U)\)

Substitute values: \(\tan(\angle U)=\frac{2.8}{1.5}\approx1.8667\).

Step3: Find \(\angle U\)

Take arctangent: \(\angle U=\arctan(1.8667)\approx61.9^\circ\).

Answer:

\(61.9\)