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3) A bird flies toward a tree limb at a 45-degree angle to the ground along a path that is 50 m long landing on the limb. Determine, in m, how high above the ground the bird is perched.

Sagot :

Answer:

35 m

Explanation:

Given :

The distance of the path from the ground to the tree limb = 50 m

The angle between the path of flight of the bird towards the tree limb and the ground = 45 degrees

Therefore we can determine the height above which the bird perched above the ground by using the rules of the trigonometric ratios as;

We know that ,

[tex]$\sin 45^\circ =\frac{\text{perpendicular}}{\text{hypothenus}}$[/tex]

[tex]$\sin 45^\circ =\frac{\text{BC}}{\text{AC}}$[/tex]

[tex]$0.7 =\frac{\text{BC}}{\text{50}}$[/tex]

[tex]\text{BC }= 0.7 \times 50[/tex]

       = 35

Therefore, the bird perched on the tree limb at a height of 35 m.

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