A ramp into a building forms a \( 7^{\circ} \) angle with the ground. If the entry point of the ramp is 6 feet from the building, how many feet long is the ramp? Round the solution the nearest hundredth. .53 feet .6 .05 feet 7.04 feet 7.96 feet

To find the length of the ramp, we can use the sine function from trigonometry. The sine of an angle in a right triangle is the opposite side over the hypotenuse. In this case, we will set up the equation: \[ \sin(7^\circ) = \frac{\text{height}}{\text{ramp length}} \] We can find the ramp length using the cosine function, where: \[ \cos(7^\circ) = \frac{\text{adjacent (distance from the building)}}{\text{ramp length}} \] Thus, we can re-arrange to find: \[ \text{ramp length} = \frac{\text{adjacent}}{\cos(7^\circ)} = \frac{6}{\cos(7^\circ)} \] Calculating \( \cos(7^\circ) \) gives approximately 0.9925. Therefore: \[ \text{ramp length} \approx \frac{6}{0.9925} \approx 6.05 \, \text{feet} \] So the closest correct answer among your options is **6.05 feet**. Ready to make some calculations? Trigonometry can feel like magic! With some practice, you'll be solving height and distance problems without breaking a sweat! In real-world applications, ramps are essential for accessibility. Whether in buildings, parks or skateboards, understanding the length and steepness of a ramp ensures safety and usability for everyone! Plus, it’s always a fun challenge to get the angles just right to meet code requirements!