Answer :
To find the height of the tree when the angle of elevation of the sun is [tex]\(68^\circ\)[/tex] and the tree casts a shadow 14.3 meters long, we can use some basic trigonometry principles, specifically the tangent function.
The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the tree in this case) to the adjacent side (the length of the shadow). We can write this as:
[tex]\[
\tan(68^\circ) = \frac{\text{Height of the tree}}{\text{Length of the shadow}}
\][/tex]
Given:
- [tex]\(\tan(68^\circ)\)[/tex] is the tangent of the angle of elevation.
- The length of the shadow is 14.3 meters.
Now, we can solve for the height of the tree:
[tex]\[
\text{Height of the tree} = \tan(68^\circ) \times 14.3
\][/tex]
When we calculate this expression, we find that the height of the tree is approximately 35.4 meters when rounded to the nearest tenth of a meter.
Therefore, the height of the tree is 35.4 meters.
The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the tree in this case) to the adjacent side (the length of the shadow). We can write this as:
[tex]\[
\tan(68^\circ) = \frac{\text{Height of the tree}}{\text{Length of the shadow}}
\][/tex]
Given:
- [tex]\(\tan(68^\circ)\)[/tex] is the tangent of the angle of elevation.
- The length of the shadow is 14.3 meters.
Now, we can solve for the height of the tree:
[tex]\[
\text{Height of the tree} = \tan(68^\circ) \times 14.3
\][/tex]
When we calculate this expression, we find that the height of the tree is approximately 35.4 meters when rounded to the nearest tenth of a meter.
Therefore, the height of the tree is 35.4 meters.
