SOLUTION: The following questions are based on trigonometry: 1. A ladder of length 4 m makes an angle of 30 degrees with the floor while leaning against one wall of a room. If the foot of t

Question 697040: The following questions are based on trigonometry:
1. A ladder of length 4 m makes an angle of 30 degrees with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60 degrees with the floor. Find the distance between these two walls of the room.
2. The length of a string between a kite and a point on the roof of a 10m high building is 180 metres. If the string makes an angle A with the level ground such that tanA = 4/3, how high is the kite from the ground?
Thank you.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
1. A ladder of length 4 m makes an angle of 30 degrees with the floor while leaning against one wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60 degrees with the floor. Find the distance between these two walls of the room.
..
You are working with 2 right triangles. On on one side you have a 30� right triangle with the 4 ft ladder as the hypotenuse. On the opposite side you have a 60� right triangle with the 4 ft ladder as the hypotenuse. Distance between the 2 walls=4cos30�+4cos60� (horizontal legs)
=4√3/2+4(1/2)
=2√3+2
..
2. The length of a string between a kite and a point on the roof of a 10m high building is 180 metres. If the string makes an angle A with the level ground such that tanA = 4/3, how high is the kite from the ground?
..
Draw a right triangle starting from a point A on the roof to the kite which becomes the hypotenuse of a right triangle with tan A= 4/3. Height of the kite=vertical leg of this right triangle plus the height of the building.
Tan A=4/3
A=53.13�
vertical leg (opp side)=180 sinA=180sin53.13�≈144
Height of the kite≈144+10≈154 m

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