Question

5) Find all unknown measures. Round lengths to the nearesthundredth and angle measures to the nearest degree..um

Answer 1

The given triangle is DEF where angle E is a right angle.

The value of DE is 2.1 and EF is 5.3.

As the triangle is a right angle triangle, hence applying the pythagoras theorem,

`\begin{gathered} DF^2=DE^2+EF^2 \\ DF^2=(2.1)^2+(5.3)^2 \\ DF^2=4.41+28.09 \\ DF^2=32.5 \\ DF=\sqrt[]{32.5} \\ DF=5.70 \end{gathered}`

Thus, the value of the side DF is 5.70 units.

The value of angle D and F can be determined as,

`\begin{gathered} \tan D=(EF)/(DE) \\ \tan D=(5.3)/(2.1) \\ \angle^{}D=68.38^(\circ) \\ \angle D\approx68^(\circ) \end{gathered}`