Question

50 POINTS Could someone please help me with this? I'm being timed. I know it's a trig question but I don't know how to set it up.
Jonathan sets a camera on a tripod to film a bird in a nest. The camera is 1.8m off the ground and 16.4m away from the tree. The angle of elevation from the camera to the bird's nest is 29°. How far above the ground is the bird's nest? Round your answer to the nearest tenth of a meter.
a) 7.3m
b) 9.1m
c) 10.9m
d) 14.3m

Answer 1

Answer: Tan29°=(n-1.8)/16.4

n=16.4tan29°+1.8

n≈10.9 meters  (to nearest tenth of a meter)

Answer 2

$\tan29^\circ=\dfrac n{16.4}$

where $n$ is the vertical distance between the nest and the camera. So the nest is

$n=16.4\tan29^\circ\approx9.09\,\mathrm m$

above the camera's position. Add 1.8 m to this to find the height of the nest above the ground, which would be

$n+1.8\,\mathrm m\approx10.9\,\mathrm m$

making the answer C.