The height of the tree is 13.82 m
Step - by - Step Explanation
What to find? Height of the tree.
Given:
• Angle of elevation = 62,°
,
• Eye-level above the ground =160cm
,
• Distance away from the tree = 6.5m
We need to first sketch the problem, to have a clearer picture of the question.
Change 160cm to meter
160 cm = 160/100 = 1.6 m
Height of the tree = 1.6 + x
We need to find the value of x.
From the sketch above;
Opposite =x
Adjacent =6.5
θ= 62°
Using the trigonometric ratio;
[tex]\tan \theta=\frac{opposite\text{ }}{\text{adjacent}}[/tex]
Substitute the values.
[tex]\tan 62=\frac{x}{6.5}[/tex]
Cross-multiply.
x=6.5tan62°
x = 12.22 m
Height of the tree = 1.6 m + 12.22m
Height of the tree = 13.82 m
OR
Height of the tree = 1382 cm approximately.
