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Solving Right Triangles
Table of Contents
Solving Right Triangles .................................................................................................................................. 2
Problem 1: Solve Right Triangle - Solve a Triangle (Easy) ......................................................................... 4
Problem 2: Solve Right Triangle - Ladder against the Building (Easy)...................................................... 4
Problem 3: Solve Right Triangle - Determine Height of Tree (Easy) ......................................................... 5
Problem 4: Solve Right Triangle - Height of a Flagpole (Easy) .................................................................. 5
Answers ......................................................................................................................................................... 6
Trigonometry
Page 1
Solving Right Triangles
Solving Right Triangles
Solving right triangles is a basic skill learned in
Trigonometry.
Solving a right triangle = determining the size of all three sides and all
angles.
These definitions will be needed to do that:
Pythagorean equation:
Where c represents the length of the hypotenuse, and a and b represent the lengths
of the other two sides.
Trigonometry
Page 2
Solving Right Triangles
Example:
John needs to determine the height of a flagpole. He determines the angle
of elevation of the top of the pole to be 20° from a point on the ground 15 ft
away from its base.
a.
Sketch the triangle. What are the angles? Find the height of the
flagpole and hypotenuse.
Solution:
Flagpole
70 degrees
c
a
15 feet
Tan 20o = a/15
(15)* Tan 20o = a
15 * .3640 = a
5.46 = a
20 degrees (elevation
angle)
height of flagpole
Cos 20o = 15/c
.9397 = 15/c
.9397 * c = 15
c = 15/.9397
c = 15.96
length of hypotenuse
Trigonometry
Page 3
Solving Right Triangles
Problem 1: Solve Right Triangle - Solve a Triangle (Easy)
One angle of a right triangle measures 30 degrees and the hypotenuse has length
10.
a. Determine the angles and sides of the triangle.
Problem 2: Solve Right Triangle - Ladder against the
Building (Easy)
A ladder leans against a building. The ladder is 12 feet long. The ladder makes an
angle of 60° with the ground.
a. How far up the wall does the ladder reach?
b. How far from the wall is the base of the ladder?
Round your answers to two decimal places.
Trigonometry
Page 4
Solving Right Triangles
Problem 3: Solve Right Triangle - Determine Height of Tree
(Easy)
Mary needs to determine the height of a tree. She measures the angle of
elevation to be 30 degrees. Her distance from the base of the tree is 10 meters.
a. How high is the tree to the nearest tenth of a meter?
Problem 4: Solve Right Triangle - Height of a Flagpole
(Easy)
John needs to determine the height of a flagpole. He determines the angle
of elevation to be 30° from a point on the ground 20 ft away from its base.
b.
Find the height of the flagpole.
Trigonometry
Page 5
Answers
Solving Right Triangles
1a: angles = 30 degrees, 60 degrees, and 90 degrees. Sides = 8.66, 5, and the
hypotenuse is 10
2a: 10.39
2b: 6.0
3a: 5.8
4a: 11.548 feet
Trigonometry
Page 6