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Section 4.3 Worksheet - Right Triangle Word Problems - Day 1
Part I Directions: Draw diagrams to illustrate the problem. Round your answer to the nearest hundredth.
1) The angle of depression is measured from the top of a 43-foot tower to a reference point on the ground. Its value is
found to be 63°. How far is the base of the tower from the point on the ground?
2) 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?
3) A closed circuit television camera is mounted on a wall 7.4 feet above a security desk in an office building. It is used
to view an entrance door 9.3 feet from the desk. Find the angle of depression from the camera lens to the entrance
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door.
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4) To illuminate the entrance of an apartment building, a night light is mounted on a 6.6 meter pole. if the base of the
pole is 24 m from the entrance, find the angle of depression from the light.
5) Driving on a flat road, you spot a mountain 28 miles away. The angle of elevation from the car to the top of the
mountain is 54°. How tall is the mountain?
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Part II Directions: Draw diagrams to illustrate the problem. Leave answer in simplest reduced radical form (NO(>ÿ .............
DECIMALS).
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6) The sun is 30° above the horizon. Find the length of a shadow cast by a silo that is 50 feet tall.
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7) The angle of elevation from the bottom of the world's longest slide, located in Peru, Vermont, is approximately °.
The slide covers a horizontal distance of 821 feet. Find the length of the slide.
8) The entrance of the old town library is 2.5 feet above the ground level. A ramp from the ground level to the library
entrance is scheduled to be built. The angle of elevation from the base of the ramp to its top is to be 30°. Find the
length of the ramp.
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9) A ladder 20 feet long leans against the side of a house. Find the height from the top of the ladder to the ground if the
angle of elevation of the ladder is 60°.
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10) A train has a 24 mile steady incline hill, at an angle of elevation of 30, that it must get over to continue on the tracks.
How tall is the hill that the train must get over to continue on the tracks?
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Name
Period
Section 4.3 Worksheet - Right Triangle Word Problems - Day 2
Patti Directions: Draw diagrams to illustrate the problem. Round your answer to the nearest hundredth.
1) The largest doors in the world are located in the Vehicle Assembly Building near Cape Kennedy, Florida. If the angle
of elevation from a point on the ground 199 feet from the base of the door is 66.6°, how high are the doors?
2) The world's longest escalator is the Leningrad Underground in Lenin Square. The escalator has an angle of elevation
of 10.36° and a vertical rise of 195.8 ft. Find the length of the escalator.
3) The world's tallest fountain is in Fountain Hills, Arizona. If the angle of elevation to the top of the fountain from a
point 755 feet from its base is 36.5°, find the height of the fountain.
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4) The sun is 25° above the horizon. Find the length of a shadow cast by a silo that is 50 feet tall.
5) The guy wire to support a radio tower is positioned 100 feet up the tower. It forms a 43° angle with the ground. How
long is the wire?
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Part II Directions: Draw diagrams to illustrate the problem. Leave answer in simplest reduced radical form (NO
DECIMALS).
6) Grain elevators are conveyor belts used throughout the Midwest to take produce, like wheat, to the top of a silo for
storage. How long would the belt of a grain elevator need to be if the bottom is 50 feet from the base of a silo that is set
at an angle of elevation of 30°?
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7) You are 5 feet tall, and your football has landed at the edge of the roof of your school building. When you are 20 feet
from the base of the building, the angle of elevation from your eyes to your football is 60°. How high off the ground is
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8) The sial slope knovÿas Devil's Hill has an angle of elevation from the ground of 45°. If the distance down the slope is
1500 meters, what is the altitude of the hill?
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9) Roof trusses often use right triangles to make a flimsy 2 x 4 more rigid to hold up the weight of the roof. If a house is
40 feet wide and the roof is an isosceles triangle with base angles of 30°, how far is it from the bottom edge of the roof
to the peak?
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i0) A ladder 20 feet long leans against the side of a house. Find the height from the top of the ladder to the ground if
the angle of elevation of the ladder is 60°.
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i2) You are 6 feet tall, and you spot a cat up in a tree. When you are 25 feet from the tree, the angle of elevation from
your eyes to the cat is 45°. How high off the ground is the cat?
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