Geometry (Triangles Pt. 2)

Question 1

Sine (Definition)

Answer 1

The trigonometric function that is equal to the ratio of the side Opposite an acute angle (In a right triangle) to the Hypotenuse.

“SOH”

*Use this equation if the side is far away from the angle

Question 2

Cosine (Definition)

Answer 2

The trigonometric function that is equal to the ratio of the side Adjacent to an acute angle (in a right triangle) to the Hypotenuse.

“CAH”

*Use this equation if the side is close to the angle

Question 3

Tangent (Definition)

Answer 3

The trigonometric function that is equal to the ratio of the side Opposite to an acute angle (in a right triangle) to the Adjacent.

“TOA”

Question 4

What is the Sin, Cos, and Tan of angle “F.”

Answer 4

Sin (F) = 12/13

Cos (F) = 5/13

Tan (F) = 12/5

Question 5

What is the Sin, Cos, and tan of angle “G.”

Answer 5

Sin (G) = 15/17

Cos (G) = 8/17

Tan (G) = 15/8

Question 6

Find the Cos of angle “A.”

Answer 6

21/29

Question 7

Tips for solving missing sides of a triangle

Answer 7

1. If the missing side is the hypotenuse, divide the given side by the Trig ratio.
2. If given the Hypotenuse, multiply the Trig ratio by the other given side.
3. If using the Tangent Function and the Opposite is given, divide by the Trig ratio.
4. If using the Tangent Function and the Adjacent is given, multiply the Trig Ratio by the other given side.

Question 8

Find the missing side of the triangle

Round your answer to the nearest hundredth.

Answer 8

6.97

Question 9

Find the missing sides of the triangle

Round your answer to the nearest hundredth.

Answer 9

x = 8.62

Question 10

Find the missing side of the triangle

Round your answer to the nearest hundredth.

Answer 10

2.26

Question 11

Find the missing angle of the triangle

Round your answer to the nearest hundredth.

Answer 11

56.25°

Question 12

Find the missing angle of the triangle

Round your answer to the nearest hundredth.

Answer 12

33.69º

Question 13

Find the missing angle of the triangle

Round your answer to the nearest hundredth.

Answer 13

51.06°

Question 14

Define the Law of Sines

Answer 14

Question 15

Tips for solving using the Law of Sines

Answer 15

1. When finding the missing angle, arcsine (Side correseponding to the missing Angle/ given side) Sine (Given angle)
2. When finding the missing side, multiply the given side by the Sine of the angle corresponding to the missing side, then divide by the Sine of the given angle.

Question 16

Find the missing angle “B”.

Answer 16

53.68°

Question 17

Find the missing side “AB”.

Answer 17

7.71

Question 18

Find the missing angle “B”.

Answer 18

60.76°

Question 19

Find the missing side “AC”.

Answer 19

9.23

Question 20

Create a proof for the Law of Sines

Answer 20

1. Create a triangle that doesn’t have a 90°
2. Label two sides and angles opposite each other.
3. Drop an altitude through the middle of the two sides and angles.
4. Create two equation using the two angles as a function of Sine.
5. Solve and simplify the two equations as a single equation for the new side “x”.

Question 21

Define the Law of Cosines

Answer 21

* The side opposite the given angle is

(The missing side squared =

side b (squared) + side c (squared) - 2(bc)cos(σ)

Question 22

Find the missing side “AB”

Answer 22

18.03

Question 23

Find the missing side “BC”.

Answer 23

14.62

Question 24

Find the missing angles

Answer 24

angle “A” = 48.37°

angle “B” = 55.30°

angle “C” = 76.33°

Question 25

Find the missing angle