Download 1) From a point on the ground 4 meters from the base of a tree, the

Trig Triangle Word Problems
1) From a point on the ground 4 meters from the base of a tree, the angle of elevation
to the top of a tree is 62  . Find the height of the tree.
2) Hikers are staying at a hotel, elevation 8,000 feet. In the morning, the hikers
follow a trail that leads from the hotel to a scenic overlook, elevation 11,100 feet.
The length of the trail is 14,100 feet. What is the inclination of the trail?
3) Two snowmobilers start from the same point and drive at 10 km/h and 12 km/h
respectively, diverging at an angle of 110  . Two hours after leaving, they find
that their radio transmissions are barely audible. How far apart are they at that
time?
4) The angle of depression from a searchlight to its target is 58  . How long is the
beam of light, if the searchlight is 26 feet above the ground?
5) A fire is sighted from two ranger stations that are 5,000 meters apart. The angles
of observation to the fire measure 52  from one station and 41 from the other
station. Find the distance along the line of sight to fire from the closer of the two
stations.
6) From a point 82 meters from the base of a telephone pole the angle of elevation to
a worker on the pole is 35  . The angle of elevation to the top of the pole is 68  .
Find the distance from the worker to the top of the pole.
7) Newton is 9 miles east of Oldtown and Littleton is 10 miles northwest of
Oldtown. How far is Newton from Littleton?
8) Two of the angles of an isosceles triangle each measure 72  . If the base measures
5.2 units, what is the height of the triangle?
9) The Statue of Liberty stands on a 150-ft pedestal. From a point 280 feet from the
base of the pedestal, the angle of elevation to the top of Liberty’s torch is 47  .
Find the height of the statue.
10) The length of the base of an isosceles triangle is 81 cm. The sides meet at a 72.4 
angle. Find the measure of the congruent sides.
11) Two streets meet at an angle of 52  . If a triangular lot has frontages of 60 meters
and 65 meters on the two streets, what is the perimeter of the lot?
12) To illuminate the entrance of a building, a night-light is mounted on a 6.6-meter
pole. If the base of a pole is 24 meters from the entrance, find the angle of
depression from the light.
13) The lengths of the sides of a triangular plot are 400 feet, 500 feet, and 700 feet.
Find the measure of the smallest angle.
14) The largest doors in the world are located in the Vehicle Assembly Building near
Cape Canaveral, FL. If the angle of elevation from a point on the ground, that is
199 feet from the base of the doors is 66.6  , how high are the doors?
15) A television antenna stands on the edge of the top of of a 52-story building. From
a point 320 feet from the base of the building, the angle of elevation to the top of
the antenna is 64  . If each story is 12 feet high, find the height of the antenna.
16) A hot air balloon is flying above Manasquan. To the left side of the balloon, the
pilot measures the angle of depression to the soccer fields to be 21 . To the right
side of the balloon, the pilot measures the angle of depression to the football field
to be 63.7  . The distance between the two fields is 1,642 km. Find the distance
from the balloon to the soccer fields.
17) The height of an isosceles triangle is 8 cm and its base is 4 cm long. Find all the
angles of the triangle.
18) Andy and Kyle leave Las Vegas at the same time. Andy drives south at 82 mph
and Kyle drives southeast at 71.3 mph. How far apart are the two guys after 3 ½
hours?
19) From a point 78 feet from the base of a tree, the angle of elevation to a cat in the
tree is 32  . The angle of elevation to the top of the tree is 72.8 . Find the
distance from the cat to the top of the tree.
20) A slide rises 28.2 feet above the ground. The length of the slide is 47.4 feet. Find
the slide’s angle of inclination.
21) An oil tanker and a cruise ship leave port at the same time and travel straight-line
courses at 10 mph and 25 mph respectively. Two hours later they are 40 miles
apart. What is the angle between their courses?
22) Two roads intersect at an angle of 102.1 . Christine’s mailbox is 476 feet from
the intersection. George’s mailbox is on the other road and is 615 feet from the
intersection. How far is it from Christine’s mailbox to George’s mailbox?
23) Two planes leave an airport at the same time, one flying due west at 500 km/h and
the other flying due southeast at 300 km/h. What is the distance between the
planes two hours later?