find ( mangle d ).\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n( mangle…

find ( mangle d ).\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n( mangle d = square^circ )

find ( mangle d ).\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n( mangle d = square^circ )

Answer

Explanation:

Step1: Identify the trigonometric ratio

In right triangle ( DEF ) (right - angled at ( E )), we know the length of the opposite side to angle ( D ) (( EF = 4 )) and the length of the hypotenuse (( DF=6 )). The sine of an angle in a right triangle is defined as ( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} ). So for angle ( D ), ( \sin(D)=\frac{EF}{DF}=\frac{4}{6}=\frac{2}{3} ).

Step2: Calculate the angle

To find the measure of angle ( D ), we take the inverse sine (arcsin) of ( \frac{2}{3} ). Using a calculator, ( D=\arcsin\left(\frac{2}{3}\right) ). Calculating this, ( \arcsin\left(\frac{2}{3}\right)\approx41.8^{\circ} ) (rounded to the nearest tenth).

Answer:

( 41.8 )