SOLUTION: 1.A Boat is viewed From top of hill Which is 2000 Ft above sea and the angle is 30 degrees. Find the distance of the observation point. 2.A small island in the middle of river whi

Question 1075710: 1.A Boat is viewed From top of hill Which is 2000 Ft above sea and the angle is 30 degrees. Find the distance of the observation point.
2.A small island in the middle of river which 100 m wide. it has a tall tree standing on it P and Q are the two points directly opposite to each other on two banks and in line with tree. Angles of P and Q is 30 degrees and 40 degrees. Find the distance of P from the tree.
Please Help me Find solution for these sums!
Thank you,
Mani.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Question #1:

2000 foot height to the observation point is vertical leg of a right triangle.
distance d, hypotenuse, distance from boat to observation point. Angle of elevation from the boat to observation point on top of hill, 30 degrees.

---------below here was wrong-- switched leg and hypotenuse by mistake-------------------

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

1.A Boat is viewed From top of hill Which is 2000 Ft above sea and the angle is 30 degrees. Find the distance of the observation point.
2.A small island in the middle of river which 100 m wide. it has a tall tree standing on it P and Q are the two points directly opposite to each other on two banks and in line with tree. Angles of P and Q is 30 degrees and 40 degrees. Find the distance of P from the tree.
Please Help me Find solution for these sums!
Thank you,
Mani.

Since the angle of depression/angle of elevation is 30^o, we have a 30-60-90 special triangle
We then have the shorter leg as 2,000 ft
If by "distance of the observation point," you mean the hypotenuse, or the distance from the boat to the top of the hill, then it's
If by "distance of the observation point," you mean the LONGER LEG, or the distance from the boat to the base (foot) of the hill, then it's
You decide!!
Whichever way, none of the lengths can be 1,000 feet, so don't even CONSIDER that, as someone has stated, as it is TOTALLY INCORRECT, as USUAL!
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