College

In ΔDEF, the measure of ∠F is [tex]90^\circ[/tex], the measure of ∠D is [tex]10^\circ[/tex], and EF = 94 feet. Find the length of DE to the nearest tenth of a foot.

Answer :

Answer:

541.3 ft

Step-by-step explanation:

The 94 foot side is opposite the 10 degree angle (see attached image), and the hypotenuse is the side you want to find.

The trigonometric ration that uses opposite and hypotenuse is sine.

Sine = opposite / hypotenuse

[tex]\sin{10^circ}=\frac{94}{x}\\\\x \sin{10^\circ}=94\\\\x=\frac{94}{\sin{10^\circ}} \approx 541.3[/tex]

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