Answer:
756.36 meters
Step-by-step explanation:
Draw a diagram. Let's call the horizontal distance from the top of the mountain to the closest point x.
Using tangent = opposite / adjacent, we can write two equations:
tan 35.3° = h / x
tan 25.76° = h / (x + 500)
Solve for x in the first equation and substitute into the second.
x = h / tan 35.3°
tan 25.76° = h / ((h / tan 35.3°) + 500)
Solve for h.
tan 25.76° (h / tan 35.3°) + 500 tan 25.76° = h
500 tan 25.76° = h (1 − (tan 25.76° / tan 35.3°))
500 tan 25.76° tan 35.3° = h (tan 35.3° − tan 25.76°)
h = 500 tan 25.76° tan 35.3° / (tan 35.3° − tan 25.76°)
h ≈ 756.36 meters
Angle A is opposite side BC
Answer: Second, Fourth and Fifth options are correct.
Step-by-step explanation:
F is the incenter because F is the point of intersection of the three angle bisector of the triangle.
As we can see that the angle bisector divides the angles into equal angles.
So, F is the point of concurrency of the angle bisectors of the angle of the triangle.
F is equidistant from the three sides of the triangle.
Hence, Second ,Fourth, Fifth options are correct.