Answer:
42.8 feet
Step-by-step explanation:
[tex]\theta=44^{\circ}[/tex]
Height of hiker=6 feet
Total height of tree=b=6+x
Distance from hiker's eye to the top of the tree=53 m
We have to find the total height of the tree.
[tex]\frac{x}{53}=sin44=0.6947[/tex]
Using the formula
[tex]\sin\theta=\frac{perpendicular\;side}{Hypotenuse}[/tex]
[tex]x=53\times 0.6947[/tex]
[tex]x=36.819[/tex]
Total height of tree= b=36.819+6=42.819=42.8 feet
Hence, the total height of tree=42.8 feet
The total height, in feet of the tree round to one decimal place is 42.8 ft.
The hiker is 6ft tall standing on the ground looking up to the top of a tree with an elevation of 44°.
The situation will form a right angle triangle. The opposite side of the triangle is part of the height of the tree(b). The distance from the hikers eye to the top of the tree is 53 ft. And this is the hypotenuse side of the triangle.
Let's find the height of the tree using trigonometric ratio
Therefore,
sin 44° = opposite / hypotenuse
sin 44° = opposite / 53
opposite = 53 sin 44°
opposite = 53 × 0.69465837045
Recall the person is 6 feet above the ground and the triangle was formed from the eyesight of the person. Therefore the height of the tree will be as follows
b = 36.8168936343 + 6
b ≈ 42.8 feet
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