**Mathematics Learning Module: Distance and Measurement Questions**---**Question 5: Measuring Distance Using Angles**A tree 1200 yards away from an observer subtends an angle of 1.5°. Use the arc length formula to estimate the height of the tree in yards.- [ ] 16 yards- [ ] 31 yards- [ ] 286 yards- [ ] 1800 yards- [ ] None of the above**Explanation:**To find the height of the tree, you can use the arc length formula, which is given by:\[ \text{Arc Length} = r \cdot \theta \]where \( r \) is the radius (or distance to the tree) and \( \theta \) is the angle in radians. First, convert the angle from degrees to radians:\[ \theta = 1.5° \times \frac{\pi}{180} = 0.02618 \text{ radians} \]Now, multiply by the distance (1200 yards):\[ \text{Height} = 1200 \times 0.02618 \approx 31.4 \text{ yards} \]Thus, the height of the tree is approximately 31 yards.---**Question 6: Calculating the Distance Between Two Cities**The cities of Vandora and Lachstan are located on the same line of longitude but at different latitudes. Vandora is on the latitude circle 35°N, while Lachstan is at 10°S. What is the distance along the surface of the Earth between the two cities? Assume that the radius of the Earth is 3700 miles. Round your answer to the nearest mile.- [ ] 3100 miles**Explanation:**Given the radius of the Earth \( R \) is 3700 miles, and the latitudinal difference (distance in degrees) between Vandora and Lachstan is:\[ |35° - (-10°)| = 45° \]We can convert this difference into radians:\[ \Delta \theta = 45° \times \frac{\pi}{180} = 0.7854 \text{ radians} \]Using the arc length formula:\[ \text{Distance} = R \cdot \Delta \theta \]\[ \text{Distance} = 3700 \times 0.7854 \approx 2905 \

Name: **Mathematics Learning Module: Distance and Measurement Questions**--
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: **Mathematics Learning Module: Distance and Measurement Questions**---**Question 5: Measuring Distance Using Angles**A tree 1200 yards away from an observer subtends an angle of 1.5°. Use the arc length formula to estimate the height of the tree in