# Math 10 Week 7

This weeks goal is to teach you how to solve an angle and side lengths in the Trigonometry Unit.

Vocabulary:

SOH: S = $\frac{O}{H}$ or Sine = $\frac{Opposite}{Hypotenuse}$

CAH: C = $\frac{A}{H}$ or Cosine = $\frac{Adjacent}{Hypotenuse}$

TOA: = $\frac{O}{A}$ or Tangent = $\frac{Opposite}{Adjacent}$

i) Question One: What is the Angle of JEP to the nearest degree? (How to find an angle knowing two side lengths)

Step 1: Label the triangle

*According to the reference angle

1. Across from the reference angle is called the opposite side (O)
2. Across from the $90^o$ angle is the hypotenuse (H)
3. And the left over side is the adjacent side (A)

Step 2: Determine which ratio to use

Use the clues from the triangle. We will be using Cosine because we have the clues from the Adjacent and hypotenuse sides. (CAH)

Step 3: Write the equation

The cos angle is unknown so we will be writing it like :

Step 4: Get the variable by itself/Solve

*when moving the COS to the other side of the equation it becomes $COS^-1$

ii) Question two: What is the side length of AP to the nearest degree. (How to find the side length of a triangle knowing one side length and one angle.)

Step 1: Label the Triangle

*According to the reference angle

Step 2: Determine the ratio

Use the clues from the triangle. We will be using Tangent because we have the clues from the adjacent and opposite sides. (TOA)

Step 3: Write the equation/Solve

*We don’t want the variable on the bottom. Reciprocate the fraction and what you do to one side you do to the other.

X= 50cm

iii) Question Three: What is the side length of AK to the nearest degree. (How to find the side length knowing one side length and one angle .)

Step 1: Label the Triangle

*According to the reference angle

Step 2: Determine the ratio

Use the clues from the triangle. We will be using Sine because we have the clues from the hypotenuse and opposite sides. (SOH)

Step 3: Write the equation/Solve

*We don’t want the variable on the bottom. Reciprocate the fraction and what you do to one side you do to the other.

X= 51 cm