As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Solution
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Answers
Let AB be the lighthouse of height 75 m. Let C and D be the positions of the ships.
30° and 45° are the angles of depression from the lighthouse.
Draw a figure based on given instructions:
To Find: CD = distance between two ships
Step 1: From right triangle ABC,
tan 45° = AB/BC
1= 75/BC
BC = 75 m
Step 2: Form right triangle ABD,
tan 30° = AB/BD
1/√3 = 75/BD
BD = 75√3
Step 3: To find measure of CD, use results obtained in step 1 and step 2.
CD = BD – BC = (75√3 – 75) = 75(√3-1)
The distance between the two ships is 75(√3-1) m. Answer!
Answer:
Let AB be the lighthouse of height 75 m. Let C and D be the positions of the ships.
30° and 45° are the angles of depression from the lighthouse.
Draw a figure based on given instructions:
To Find: CD = distance between two ships
Step 1: From right triangle ABC,
tan 45° = AB/BC
1= 75/BC
BC = 75 m
Step 2: Form right triangle ABD,
tan 30° = AB/BD
1/√3 = 75/BD
BD = 75√3
Step 3: To find measure of CD, use results obtained in step 1 and step 2.
CD = BD – BC = (75√3 – 75) = 75(√3-1)
The distance between the two ships is 75(√3-1) m.