Explain Trigonometry

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syrzvatprs

Mathematics

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  1. Is it possible to solve the dimensions of any triangle when given the lengths of two sides and one angle of the triangle? Be ready to go over an example of a triangle you have created and solve for the missing dimensions.
  2. What would be different if the triangle you were trying to solve was a right triangle? Be ready to go over an example of a triangle you have created and solve for the missing dimensions.
  3. Is it possible to solve the dimensions of any triangle when given the length of one side and two angles of the triangle? Be ready to go over an example of a triangle you have created and solve for the missing dimensions.
  4. You are building a house and are making a drawing of the kitchen. The sink is 3 feet away from the dishwasher, and the sink is 8 feet away from the fridge. The included angle between the distances is 48Β°. How far away is the dishwasher from the fridge? Explain. Are these reasonable dimensions for a kitchen? If not, what would you change?

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Explanation & Answer

Here is my answer :)

Explain Trigonometry

1. Is it possible to solve the dimensions of any triangle when given the lengths of two sides
and one angle of the triangle? Be ready to go over an example of a triangle you have
created and solve for the missing dimensions.
If we know the lengths of two sides and one angle of a triangle we can solve the dimensions of it.
For this we can use two of these rules:

-

Sine rule
𝛼
𝑏
𝑐
=
=
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐡 𝑠𝑖𝑛𝐢

-

Cosine rule
π‘Ž2 = 𝑏 2 + 𝑐 2 βˆ’ 2𝑏𝑐 βˆ— π‘π‘œπ‘ π΄
𝑏 2 = π‘Ž2 + 𝑐 2 βˆ’ 2π‘Žπ‘ βˆ— π‘π‘œπ‘ π΅
𝑐 2 = 𝑏 2 + π‘Ž2 βˆ’ 2π‘π‘Ž βˆ— π‘π‘œπ‘ πΆ

For example, if we have the following triangle:
C
a

b=3

B
A = 30β—¦
To solve this triangle we can use the cosine rule
to
find
the
side
a:
c=4
π‘Ž2 = 𝑏 2 + 𝑐 2 βˆ’ 2𝑏𝑐 βˆ— π‘π‘œπ‘ π΄

π‘Ž2 = 32 + 42 βˆ’ 2 βˆ— 3 βˆ— 4 βˆ— π‘π‘œπ‘ 30
π‘Ž = 2.05

Then using the sine rule, we can find the angle B
𝛼
𝑏
=
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐡
2.05
3
=
𝑠𝑖𝑛30 𝑠𝑖𝑛𝐡
𝐡 = 46.94°

Finally we know that the sum of the angles of a triangle is equal to 180. We can find the angle C
by:
𝐴 + 𝐡 + 𝐢 = 180°
30 + 46.94 + 𝐢 = 180°
𝐢 = 103.064°
2. What would be different if the triangle you were trying to solve was a right triangle? Be
ready to go over an example of a triangle you have created and solve for the missing
dimensions.
If the triangle was a right triangle we can solve it easily using the Pythagorean Theorem knowing
that a and b are sides, and c is the hypotenuse of the triangle:
B
...


Anonymous
Great study resource, helped me a lot.

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