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The picture shows a triangular island:

A right triangle is shown with an acute angle equal to 65 degrees. The length of the side of the triangle opposite to the acute angle is f. The length of the side of the triangle adjacent to the acute angle is d. The length of the hypotenuse is e.

Which expression shows the value of e?
f sin 65°
f cos 65°
d over cos 65 degrees
d over sin 65 degrees

Respuesta :

samia2020
Answer:
d over cos 65 degrees

Explanation:
cos65 = d/e
e = d / cos65
boffeemadrid

Answer:

(C) [tex]\frac{d}{cos 65^{\circ}}[/tex].

Step-by-step explanation:

It is given that a right triangle PQR with an acute angle equal to 65° that is ∠QPR, PQ=d, PR=e and QR=f

Now, using trigonometry, we have

[tex]cos65^{\circ}=\frac{PQ}{PR}[/tex]

Substituting the given values, we get

[tex]cos 65^{\circ}=\frac{d}{e}[/tex]

[tex]e=\frac{d}{cos 65^{\circ}}[/tex]

Thus, the value of e is [tex]\frac{d}{cos 65^{\circ}}[/tex].

Hence, option (C) is correct.

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