A solution can be found using substitution by substituting the ordered pair into both of the original equations.
Answer: The height of the mountain is 1,331.4 meters (approximately)
Step-by-step explanation: From the information given, the students were standing at point b which is 800 meters from the base of the mountain and the angle of elevation from that point is 59°. Assuming that the ground is level, we can derive a right angled triangle from this set of details and hence we have triangle ABC, where angle β is the reference angle, (59 degrees), BC is the distance from the students to the base of the mountain (800 meters) and the line AC is the height of the mountain.
The line AC is the opposite, since angle B is the reference angle, therefore we shall use the trigonometric ratio as follows;
Tan β = opposite/adjacent
Tan 59 = AC/800
Tan 59 x 800 = AC
1.6643 x 800 = AC
1331.44 = AC
AC ≈ 1331.4
Therefore the height of the mountain is approximately 1,331.4 meters
