Question

Two girls are standing 100 feet apart they both see a beautiful seagull in the air between them the angles of elevation from the girls to the bird are 20 degrees and 45 degrees respectively how high up is the seagull

Answer 1

`26.68\ \text{feet}`

Explanation:

a = 100 feet

`\angle B=20^(\circ)`

`\angle C=45^(\circ)`

`\angle A=180-(20+45)=115^(\circ)`

From sine rule we have

`(\sin B)/(b)=(\sin A)/(a)\\\Rightarrow b=(\sin B)/(\sin A)a\\\Rightarrow b=(\sin 20^(\circ))/(\sin 115^(\circ))* 100\\\Rightarrow b=37.73\ \text{feet}`

`\sin C=(h)/(b)\\\Rightarrow h=b\sin C\\\Rightarrow h=37.73* \sin 45^(\circ)\\\Rightarrow h=26.68\ \text{feet}`

The is seagull is
`26.68\ \text{feet}` above the ground.