Given a right triangle with an angle of $35°$ and an adjacent side of length $5$, which equation can be used to solve for the hypotenuse $c$?

• A. $c=\frac{5}{cos(35°)}$
• B. $c=5\cdot cos(35°)$
• C. $c=5\cdot sin(35°)$
• D. $c=\frac{5}{sin(35°)}$

Answer: (A)

Verified step by step guidance

1. Identify the sides of the right triangle relative to the given angle of 35°: the side of length 5 is adjacent to the angle, and the hypotenuse is the side opposite the right angle, labeled as \( c \).
2. Recall the definition of cosine in a right triangle: \( \cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}} \). Here, \( \theta = 35^\circ \), the adjacent side is 5, and the hypotenuse is \( c \).
3. Set up the equation using the cosine ratio: \( \cos(35^\circ) = \frac{5}{c} \).
4. To solve for \( c \), multiply both sides of the equation by \( c \) and then divide both sides by \( \cos(35^\circ) \) to isolate \( c \): \( c = \frac{5}{\cos(35^\circ)} \).
5. This equation \( c = \frac{5}{\cos(35^\circ)} \) can be used to find the length of the hypotenuse given the adjacent side and the angle.