Lisa spots a mother bird on a branch above the nest in the diagram. She measures an angle of elevation to the bird (the small oval on the diagram) of 67º. Find how high the mother bird is above the ground. Round to the nearest foot. (** Hint**: Draw and label the new triangle with the mother bird at the top, before solving the problem.)

Guest Oct 6, 2014

#1**+5 **

You have a right-angled triangle in which the height (the item you want to find) is *opposite* the known angle. You also know the *adjacent* length to the angle.

This means you should use the tan function; tan(angle) = opposite/adjacent.

Here: tan(62°) = height/15

Multiply both sides by 15: height = 15*tan(62°) ft

$${\mathtt{height}} = {\mathtt{15}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{62}}^\circ\right)} \Rightarrow {\mathtt{height}} = {\mathtt{28.210\: \!896\: \!980\: \!19}}$$

So height = 28 ft to the nearest foot.

Alan
Oct 6, 2014

#2**+5 **

Remember your SOH CAH TOA.

Here you have the angle and the Alternate side of the triangle. So use the Tangent function.

Tan (61˚)=Opposite/Alternate

Tan (61˚)=O/15ft

O=Tan(61˚) *15= 27.06 ft.

Guest Oct 6, 2014

#3**+10 **

Best Answer

It appears that, from the illustration, that the bird is above the nest...if I'm interpreting the picture correctly. The angle of elevation to the nest is 62°, but the angle of elevation to the bird itself is 67°.

So we have

Height above ground = 15*tan(67°) = about 35.34 ft.

CPhill
Oct 6, 2014