Question

maeva is standing 40 meters from the foot of a tree. her line of sight to the top of the tree forms an angle of elevation of 55*. find the approximate height of the tree above maeva's line of sight.
a. 46.15 m
b. 65.55 m
c. 28.01 m
d. 57.13 m

Answer 1

To find the height of the tree above Maeva's line of sight, we can use the tangent of the angle of elevation. The formula for tangent in a right triangle is:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case:
- \(\theta = 55^\circ\)
- The distance from Maeva to the tree (the adjacent side) is 40 meters.
- The height of the tree above Maeva's line of sight is the opposite side that we want to find.

Rearranging the formula gives us:

\[
\text{opposite} = \tan(\theta) \times \text{adjacent}
\]

Substituting the known values:

\[
\text{height} = \tan(55^\circ) \times 40 \, \text{m}
\]

Now we calculate the value:

\[
\tan(55^\circ) \approx 1.4281 \quad (\text{using a calculator})
\]

So,

\[
\text{height} = 1.4281 \times 40 \approx 57.12 \, \text{m}
\]

Thus, the approximate height of the tree above Maeva's line of sight is:

**d. 57.13 m**