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Anna007 [38]
3 years ago
14

Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50

º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground. NextReset

Mathematics
2 answers:
attashe74 [19]3 years ago
8 0

Answer:

The bird is at a height of 1.95 km from the ground.

Step-by-step explanation:

It is given that the distance between susan and mark is 7 km and bird is between  susan and mark. The angles of elevation they make are 20º and 50º, respectively.

Draw a perpendicular line from the bird on base.

Let the distance of susan from and the altitude be x.

In triangle ABS,

tan(20^{\circ})=\frac{AB}{x}

tan(20^{\circ})x=AB

0.364x=AB       ..... (1)

In triangle ABM,

tan(50^{\circ})=\frac{AB}{7-x}

1.192(7-x)=AB     ..... (2)

From (1) and (2), we get

0.364x=1.192(7-x)

1.556x=8342

x=5.36

The length of AB is,

AB=0.364(5.36)=1.95147\approx 1.95

Therefore, the he bird is at a height of 1.95 km from the ground.

NemiM [27]3 years ago
7 0
The answer is 1.952 km
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