Problem

In $\triangle \mathrm{DEF}, d=6.9 \mathrm{~cm}, f=5 \mathrm{~cm}$ and $\angle \mathrm{F}=44^{\circ}$. Find all possible values of $\angle \mathrm{D}$, to the nearest 1oth of a degree.

Solution

Step 1 :Use the Law of Sines: \(\frac{d}{\sin(D)} = \frac{f}{\sin(F)}\)

Step 2 :Plug in the given values: \(\sin(D) = \frac{6.9 \times \sin(44)}{5}\)

Step 3 :Calculate the sine of angle D: \(\sin(D) \approx 0.9586\)

Step 4 :Find angle D using arcsine: \(D \approx 74.0°\) and \(D \approx 106.0°\)

Step 5 :\(\boxed{\text{Final Answer: Angle D has two possible values: approximately 74.0° and 106.0°}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/11414/

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