-Two ships are sailing in the sea on either side of a lighthouse. The angle of elevation of the top of the lighthouse as observed from the ships are 30 deg and 45° respectively. If the lighthouse is 200 m high, find the distance between the two ships. (sqrt(3) = 1.732)

theres 2 ways to do this. the way that doesnt require thinking is using tan to find the distance between the boats. X and Y are the distances from the boat to the lighthouses respectively.

Boat 1:

tan45degrees=200/x

x=200/tan45degrees

x=200

Boat 2:

tan30degrees=200/y

y=200/tan30degrees

y=200sqrt3

you add the distances to get the distance between the 2 boats, 200+200sqrt3

method 2:

this method requires basic knowledge of triangles. In this problem there are coincidentally a 45-45-90 triangle, and a 30-60-90. These 2 triangles have special properties to easily find the sides.

for the 45-45-90 triangle, you know its iscoseles. Thus, the height of the lighthouse(one leg) is the same as the distance from the boat to the lighthouse(the other leg). so its 200. Btw the ratios between the sides are (leg,leg,hypotenuse) x, x, xsqrt2. so if you know one of the legs is 100 the you times it by sqrt 2 to get the hypotenuse.

for the 30-60-90 triangle, the property is (short leg, long leg, hypotenuse) x, xsqrt3, 2x. The short leg in the problem is 200. thus to get the long leg, (the distance from the boat to the tower) is 200 times sqrt3.

so its 200+200sqrt3.

hope this helps.

-Two ships are sailing in the sea on either side of a lighthouse. The angle of elevation of the top of the lighthouse as observed from the ships are 30 deg and 45° respectively. If the lighthouse is 200 m high, find the distance between the two ships. (sqrt(3) = 1.732)​

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-Two ships are sailing in the sea on either side of a lighthouse. The angle of elevation of the top of the lighthouse as observed from the ships are 30 deg and 45° respectively. If the lighthouse is 200 m high, find the distance between the two ships. (sqrt(3) = 1.732)