NAME_____________________________________DATE_______________________
TRIGONOMETRY WORD PROBLEMS
MRS. BINASO
For each of the following, draw a picture and answer the question on loose leaf.
1. Wire braces are needed for the 80-foot ridgepole of a circus tent. Each brace is supposed to make a
60 angle with the ground. Find, to the nearest foot, how long each brace should be.
2.
At a point 40 feet from the foot of an oak tree, the angle of elevation to the top of the tree is 42. Find
the height of the tree to the nearest foot.
3.
In a Rochester parking garage, the levels are 23 feet apart. Each up-ramp to the next level is 144 feet
long. Find the measure of the angle of elevation of the incline for each ramp to the nearest tenth of a
degree.
4.
Since the distance across Smokey Swamp cannot be measured directly, Margaret (at point M) uses her
knowledge of trigonometry. Using the accompanying diagram and the indicated measurements, find,
to the nearest meter, the distance across the swamp.
5.
If the diagonal of a rectangular sundeck makes an angle of 67 with one side of the deck and the length
of the diagonal is 24 feet, what are the dimensions, to the nearest foot, of the sundeck?
6. A ladder leaning against a house makes an angle of 70 with the ground. If the
ladder is 25 feet long, find, to the nearest foot:
a. how far the foot of the ladder is from the base of the house
b. how high above the ground the ladder touches the house
7.
Ken's distance from Jericho’s water tower is 1,000 feet. If Ken is 6 feet tall and his eyes sight the top
of the tower at an angle of 30, what is the height of the tower?
8.
A kite is flying at the end of a taut 175-foot string. Patricia, who is 5 feet tall, holds the string, which
reaches up into the air at an angle of 75 with the horizontal. Find, to the nearest foot, how high above
the ground the kite is.
9.
Find the value of x using the accompanying diagram of isosceles trapezoid ABCD.
10. In the accompanying diagram of rhombus ABCD, the obtuse angle of the rhombus is 150 and the
shorter diagonal is 10 units. Find, to the nearest tenth, the value of each side. Also, find the value of
the longer diagonal to the nearest tenth.