Question

Triangle DEF contains right angle E. If angle D measures 55° and its opposite side measures 7.6 units, what is the measure of side
DF? Round your answer to the nearest hundredth.

A. 5.34 units
B. 6.38 units
C. 9.06 units
D. 9.28 units

Answer 1

Answer:

D. 9.28 units

Step-by-step explanation:

DF is the hypotenuse of the triangle.

$\frac{sin(A)}{a} =\frac{sin(B)}{b}$

$\implies \frac{sin(55)}{7.6} =\frac{sin(90)}{DF}$

$\implies DFsin(55) =7.6sin(90)$

$\implies DF =\frac{7.6sin(90)}{sin(55)}$

$\implies DF =9.277886875...$

$\implies DF =9.28\ \textsf{units (nearest hundredth)}$