Right Triangle Trigonometry
o Use the Right Triangle Trigonometry Functions
to evaluate angles of right triangles. Find the exact values of the six trig functions of the
The Right Triangle Trigonometric Functions 3
opp adj opp 4
sin θ = cos θ = tan θ =
hyp hyp adj
hyp hyp adj
csc θ = sec θ = cot θ =
opp adj opp
Many applications of trigonometry involve a process 6
called solving right triangles. In this type of θ
application, you are usually given one side of a right
triangle and one of the acute angles and asked to
find one of the other sides, or you are given two
sides and asked to find one of the acute angles.
Many times it is very helpful to draw a diagram to
help organize your thoughts and help visualize the
Page 1 of 2
Right Triangle Trig 1
5 Sketch the right triangle corresponding to the
1. Find the exact values of the six 3
trigonometric functions of the trigonometric function of the acute angle θ. Use the
angle θ shown. (Use the Pythagorean Theorem o determine the third side and
Pythagorean Theorem to find the then find the other five trigonometric functions of θ.
third side of the triangle.
2. Find the exact values of the six 2.5 3
5. sin θ =
trigonometric functions of the θ 4
angle θ for each of the triangles. 2 10
Explain why the function values
are the same. θ
Sketch a right triangle corresponding to the trigonometric
function of the acute angle θ. Use the Pythagorean
Theorem to determine the third side and then find the
other five trigonometric functions of θ .
2 6. sec θ = 2
3. sin θ = 4. tan θ = 3
Construct an appropriate triangle to complete the table.
≤ θ ≤ 90 , 0 ≤ θ ≤
Function θ (deg) θ (rad)
5. sin 30°
6. tan 45° 7. tan θ = 3
Use a calculator to evaluate each function. Round your 3
answers to four decimal places. 8. cot θ =
π π 2
10. cot 11. tan
12. A 30-meter line is used to tether a helium-filled balloon.
Because of a breeze, the line makes an angle of
approximately 75° with the ground. What is the height
of the balloon?
13. A biologist wants to know the width w of a river in 9. A surveyor is standing 50 feet from the base of a
order to set up instruments for studying the pollutants
in the water. From point A, the biologist walks
large tree. The surveyor measures the angle of
downstream 100 feet to point B and sights to point C. elevation to the top of the tree as 71.5°. How tall
From this sighting, it is determined that θ = 58 . How is the tree?
wide is the river?
14. In traveling across flat land, you notice a mountain
directly in front of you. Its angle of elevation to the
peak is 3.5°. After you drive 13 miles closer to the
mountain, the angle of elevation is 9°. Approximate the
height of the mountain.