The training of a football team involves running up and down a sandhill 25 times. If the hill is 30 m high and inclined at an angle of 35 degrees to the horizontal, how far does the team run during the training? Answer to the nearest 0.1 km.
the length x of the hill is found via
30/x = sin35°
you can take it from there, right?
Yes I can. Thank you
To find out how far the team runs during the training, we need to calculate the total distance covered while running up and down the sandhill.
Step 1: Calculate the horizontal distance covered while running up the sandhill.
The horizontal distance covered can be found using trigonometry. We can use the angle of inclination and the height of the sandhill to calculate this distance. The horizontal distance (d) covered while running up the hill is given by:
d = height * tangent(angle)
d = 30 * tangent(35 degrees)
Step 2: Calculate the distance covered while running down the sandhill.
Since the team goes back down the same sandhill, the distance covered while running down will be the same as running up. So, the distance covered while running down is also given by:
d = 30 * tangent(35 degrees)
Step 3: Calculate the total distance covered by summing up the distance covered while running up and down the sandhill.
Total distance = distance running up + distance running down
Total distance = 2 * (30 * tangent(35 degrees))
Step 4: Convert the total distance to kilometers.
Since the provided answer needs to be rounded to the nearest 0.1 km, we need to convert the distance to kilometers and round accordingly.
Total distance in kilometers = (2 * (30 * tangent(35 degrees))) / 1000
By performing these calculations using the appropriate mathematical functions in a calculator or a programming language, we can find the answer to the nearest 0.1 km.