Download Using Trig to Solve for Missing Sides

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Date: __________________
Using Trigonometry to Solve for Missing Sides
Algebra 1
Right triangle trigonometry was developed in order to find missing sides of right triangles, similar to
the Pythagorean Theorem. The key difference, though, is that with trigonometry as long as you have
one side of a right triangle and one of the acute angles, you can then find the other two missing sides.
TRIGONOMETRIC RATIOS
Recall that in a right triangle with acute angle A, the following ratios are defined:
sin A =
opposite
hypotenuse
cos A =
adjacent
tan A =
hypotenuse
Exercise #1: For the right triangle below it is known that sin A =
opposite
adjacent
3
. Find the value of x.
4
20
x
A
Exercise #2: In the right triangle below, find the length of AB to the nearest tenth.
C
26
38
B
A
The key in all of these problems is to properly identify the correct trigonometric ratio to use.
Exercise #3: For the right triangle below, find the length of BC to the nearest tenth.
B
65
A
Algebra 1, Unit #8 – Right Triangle Trigonometry – L5
The Arlington Algebra Project, LaGrangeville, NY 12540
12
C
Exercise #4: In each triangle below, use the appropriate trig function to solve for the value of x.
Round to the nearest tenth. Triangles are not drawn to scale.
(a)
(b)
50
x
15
42
x
8
Exercise #5: Which of the following would give the length of BC shown below?
(1) 18sin ( 34 )
(3)
C
18
cos ( 34 )
18
(2)
18
sin ( 34 )
(4) 18 tan ( 34 )
34
A
B
Exercise #6: A ladder leans against a building as shown in the picture below. The ladder makes an
acute angle with the ground of 72°. If the ladder is 14 feet long, how high, h, does the ladder reach up
the wall? Round your answer to the nearest tenth of a foot.
14 feet
h
72 Algebra 1, Unit #8 – Right Triangle Trigonometry – L5
The Arlington Algebra Project, LaGrangeville, NY 12540
Name: ____________________________________
Date: __________________
Using Trigonometry to Solve for Missing Sides
Algebra 1 Homework
Skill
In problems 1 through 3, determine the trigonometric ratio needed to solve for the missing side and
then use this ratio to find the missing side.
1. In right triangle ABC, m∠A = 58 and AB = 8 . Find the length of each of the following. Round your
answers to the nearest tenth.
C
(a) BC
(b) AC
A
58
8
B
2. In right triangle ABC, m∠B = 44 and AB = 15 . Find the length of each of the following. Round
your answers to the nearest tenth.
(a) AC
B
44 15
(b) BC
C
A
3. In right triangle ABC, m∠C = 32 and AB = 24 . Find the length of each of the following. Round
your answers to the nearest tenth.
B
(a) AC
24
32
(b) BC
Algebra 1, Unit #8 – Right Triangle Trigonometry – L5
The Arlington Algebra Project, LaGrangeville, NY 12540
C
A
4. Which of the following would give the length of hypotenuse PR in the diagram below?
(1) 8 cos ( 24 )
(2)
8
cos ( 24 )
(3) 8 tan ( 24 )
(4)
R
8
tan ( 24 )
24
Q
8
P
Applications
5. An isosceles triangle has legs of length 16 and base angles that measure 48°. Find the height of the
isosceles triangle to the nearest tenth. Hint – Create a right triangle by drawing the height.
16
16
48°
48°
6. Carlos walked 10 miles at an angle of 20 north of due east. To the nearest tenth of a mile, how far
east, x, is Carlos from his starting point?
N
10 miles
20
E
x
7. Students are trying to determine the height of the flagpole at Arlington High. They have measured
out a horizontal distance of 40 feet from the flagpole and site the top of it at an angle of elevation of
52 . What is the height, h, of the flagpole? Round your answer to the nearest tenth of a foot.
h
52 Algebra 1, Unit #8 – Right Triangle Trigonometry – L5
The Arlington Algebra Project, LaGrangeville, NY 12540
40 ft