Hey.

From a point A on the ground, the angle of elevation to the top of a tree is 52 degrees. If the tree is 14.8m away from point A, find the height of the tree.

The correct answer is 18.94 m

Can anyone show me how to do this problem?

Note: the diagram attached below is how I think it should look like based on the question.

2. Originally Posted by fabxx
Hey.

From a point A on the ground, the angle of elevation to the top of a tree is 52 degrees. If the tree is 14.8m away from point A, find the height of the tree.

The correct answer is 18.94 m

Can anyone show me how to do this problem?

Note: the diagram attached below is how I think it should look like based on the question.

$\displaystyle \tan(\theta) = \frac{opposite \, \,side}{adjacent \, \, side}$

$\displaystyle \tan(52) = \frac{x}{14.8}$

$\displaystyle x = 14.8 \tan(52) = 18.9$

3. Originally Posted by skeeter
$\displaystyle \tan(\theta) = \frac{opposite \, \,side}{adjacent \, \, side}$

$\displaystyle \tan(52) = \frac{x}{14.8}$

$\displaystyle x = 14.8 \tan(52) = 18.9$
But the 52 degrees is outside the triangle. Shouldn't it be 90 degrees minus 52 degrees which equal 48 degrees.

And use tan48 to solve?

I don't quite get it. Thanks in advance

4. Originally Posted by fabxx
But the 52 degrees is outside the triangle. Mr F says: No it's not. Are you familiar with the definition of angle of elevation?

Shouldn't it be 90 degrees minus 52 degrees which equal 48 degrees.

And use tan48 to solve?

I don't quite get it. Thanks in advance
Originally Posted by fabxx
the angle of elevation to the top of a tree is 52 degrees
Regardless of how the diagram looks, angle of elevation = 52 degrees means that the 52 degrees is inside the triangle and is used as explained in post #2.

5. Originally Posted by fabxx
But the 52 degrees is outside the triangle. Shouldn't it be 90 degrees minus 52 degrees which equal 48 degrees.

And use tan48 to solve?

I don't quite get it. Thanks in advance