Question

4. a grass airstrip runs from north to south. dave notes that there are trees off the southern end at an unknown distance reasoning and proving tools problem solving communicating and an unknown height. he would like to determine the height of the trees. from the departure point of the runway, the angle of elevation of the tallest tree is 40. dave walks 100 m west and notes that the base of the tree and the departure point of the runway are separated by an angle of 830. a) draw a diagram to model this situation, labelling all measurements. b) what will you calculate first? what tool will you use? perform the calculation. c) determine the height of the tallest tree. d) dave consults his aircraft's operating manual and, taking air temperature into account, calculates that his plane can climb at a rate of 75 m per kilometre of horizontal distance flown. is it safe for dave to attempt a takeoff and climb out straight ahead? justify your answer.

Answer 1

The student's question is solved by drawing trigonometric diagrams, calculating distances using angles and known lengths, and then comparing the aircraft's climb rate with the obstacle clearance to assess takeoff safety.

Step-by-step explanation:

The student's question pertains to using trigonometry to determine the height of a tree and assessing the safety of an airplane takeoff. To approach this problem, one would need to create a diagram including triangles formed by Dave's observations, and use trigonometric functions to find the height of the tree.

Tools like a calculator with trigonometry functions will be used. The first calculation would involve finding the distance from Dave to the base of the tree after he moves 100 m west. Then, using the angle of elevation, one would calculate the height of the tree.

Regarding Dave's aircraft takeoff, we compare the rate of climb to the obstacle clearance required. If the rate of climb is sufficient to clear the height of the trees, it would be safe to attempt takeoff and climb out straight ahead. To confirm this, we compare Dave's plane climb rate, provided by the aircraft's operating manual, to the needed rate of climb obtained from the tree height and distance calculations.