Subjects trigonometry

Triangle Sides

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Triangle Sides


1. **Problem (c):** Given an angle of 60° and the hypotenuse (or a side) of 20 meters, solve for the adjacent side or other relevant side. 2. Since the problem statement lacks explicit sides, if we assume 20 meters is the hypotenuse and the angle 60° is between the hypotenuse and the adjacent side, we can use the cosine function: $$ \cos 60^\circ = \frac{\text{adjacent side}}{20} $$ 3. Calculate cosine of 60°: $$ \cos 60^\circ = 0.5 $$ 4. Find the adjacent side: $$ \text{adjacent side} = 20 \times 0.5 = 10 \text{ meters} $$ --- 5. **Problem (d):** Given a side length of 7 cm and an angle of 45°, solve for the unknown side $x$. 6. If the 7 cm is the adjacent side to the angle 45°, and we want to find the opposite side $x$, use the tangent function: $$ \tan 45^\circ = \frac{x}{7} $$ 7. Calculate tangent of 45°: $$ \tan 45^\circ = 1 $$ 8. Find $x$: $$ x = 7 \times 1 = 7 \text{ cm} $$ **Final answers:** - For (c), the adjacent side is 10 meters. - For (d), the side $x$ is 7 cm.