Answer:
[tex]\boxed {\boxed {\sf 260 \ feet}}[/tex]
Step-by-step explanation:
We are asked to find the driver's altitude increase. The increase in altitude is also the height of the triangle, which is labeled a.
Since this is a right triangle (signified by the small square representing a 90 degree angle), we can use trigonometry. The three trigonometric ratios are:
- sinθ=opposite/hypotenuse
- cosθ= adjacent/hypotenuse
- tanθ=opposite/adjacent
The angle (θ) given is 3 degrees. Side a is opposite this angle and the side measuring 4,960 feet is the hypotenuse because it is opposite the right angle. Therefore, we use sine.
[tex]sin \theta= \frac {opposite}{hypotenuse}[/tex]
[tex]sin 3= \frac {a}{4960}[/tex]
We are solving for a, so we must isolate the variable. It is being divided by 4960 and the inverse of division is multiplication. Multiply both sides by 4960.
[tex]4960*sin 3= \frac {a}{4960}*4960[/tex]
[tex]4960*0.05233595624= a[/tex]
[tex]259.586343=a[/tex]
Round to the nearest whole number. The 5 in the tenth place tells us to round the 9 to a 0 in the ones place, then the 5 to a 6 in the tens place.
[tex]260 \approx a[/tex]
The driver's increase in altitude is approximately 260 feet.
