To estimate the height of a tree, a forester uses a device about 6 ft off the gr

Question

To estimate the height of a tree, a forester uses a device about 6 ft off the ground and finds that the angle of elevation to the top of the tree is about 39 degree Then when she moves about 80 ft closer, then angle of elevation increases about 53 degree About how tall is the tree? Two kids, Biff and Zork*, are mad at their parents for pressuring them to get straight A's. So they take their feelings out on innocent people, and risk being sent to Juvenile Court, by shining laser pointers at a hot air balloon. Biff is 1601 feet west of Zork, and the angles of elevation from Biff and Zork to the balloon are 64 degree and 50 degree, respectively. How far are they from the balloon, and how long would it take the light beam from the closer pointer to hit the balloon if the speed of light in this part of the galaxy is slowed to 120 ft/sec**? Where did I get these names from? Or, more grammerraticaly, from where might I have gotten these names? ** See the very fun sci-fi novel "A Fire Upon the Deep" (Vernon Vinge), which probably doesn't say that, but has as one premise some other strange things that happen as one gets closer and closer to the galactic centre.

Explanation / Answer

1) let height of the tree is h feet

applying tan rule on outer triangle

tan 39 = h / x + 80

(x+80) tan 39 = h ---------------- equation 1

now applying tan rule on inner triangle

tan 53 = h / x

h = tan 53 * x ------------ equation 2

setting 2 equations equal to each other

(x+80) tan 39 =  tan 53 * x

x tan 39 + 80 tan 39 = x tan 53

80 tan 39 = x ( tan 53 - tan 39 )

x = 80 tan 39 / ( tan 53 - tan 39 )

x = 125.242

h = tan 53 ( 125.242)

h = 166.20 feet

height of the tree is 166.20 feet ( approx)

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