Question

5: Using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. The telescope is positioned so thät the of si ne ght to the eagle forms a 38e angle of elevation. The telescope sits 1.3 m above the ground and the base of the telescope is 116 m from the base of the cliff. To the nearest tenth of a meter, how high above the ground is the eagle?
A 90.6 m B 91.9 m C 148.5 m D 149.8 m

Answer 1

The telescope the cliff and the eagle will from a right tingle as you can see in the picture. The distance between the base of the cliff an the telescope will be the adjacent side of the elevation angle. 
The opposite side of the elevation angle will be the height of the cliff 1.3 meters above the ground.
Now, to find the opposite side, $a$, of our elevation angle, we are going to use the trig function tangent:
$tan(38)= \frac{a}{116}$
$a=116tan(38)$
$a=90.6$

Finally, we are going to add the height of the telescope and the height of the cliff above the ground:
$90.6+1.3=91.9$

We can conclude that the eagle is 91.9 meters above the ground; therefore, the correct answer is B 91.9 m