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

Explanation:

Step1: Identify the triangle type and sides

We have a right - triangle ( \triangle BDC ) with ( \angle D = 90^{\circ} ), ( BD = 4 ) (opposite to ( \angle C )) and ( CD = 9 ) (adjacent to ( \angle C )). To find ( \angle C ), we can use the tangent function, where ( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} ). So, ( \tan(\angle C)=\frac{BD}{CD}=\frac{4}{9} ).

Step2: Calculate the angle

To find ( \angle C ), we take the arctangent (inverse tangent) of ( \frac{4}{9} ). Using a calculator, ( \angle C=\arctan\left(\frac{4}{9}\right) ). Calculate ( \frac{4}{9}\approx0.4444 ), then ( \arctan(0.4444)\approx23.9^{\circ} ) (rounded to the nearest tenth).

Answer:

( 23.9 )