Sine Ratio

Understanding the tanget, cosine, and sine ratios

Objectives

• Understand sine, cosine and tangent ratios

  for right triangles

• Calculate sine, cosine and tangent ratios

  for right triangles

Review 1

Name of sides of a right-angled triangle

Review 2

Pythagorean Theorem

Multiple Choice

In this triangle, hypotenuse is ...

• LM

• LN

• MN

Multiple Choice

In this triangle, adjacent side of angle

$$\theta$$  is  ...

• LM

• LN

• MN

Multiple Choice

In this triangle, opposite side of angle

$$\theta$$  is ...

• LM

• LN

• MN

Multiple Choice

The length of QR in right-angled triangle PQR is...

• 24 cm

• 26 cm

• 14 cm

• 16 cm

Trigonometric Ratios

Comparing the length of two sides related to angle

 $\theta$  

Example 1

•  $\tan\ A=\frac{3}{4}$  

•  $\tan\ B=\frac{4}{3}$  

•  $\sin A=\frac{3}{5}$  

•  $\cos A=\frac{4}{5}$  

•  $\cos B=\frac{3}{5}$  

Example 2

• Given

   $\tan A=\frac{8}{5}$  , what is the length of AC?

•  $\tan A=\frac{BC}{AC}=\frac{8}{5}$  

•  $\frac{16}{AC}=\frac{8}{5}$  

•  $AC=\frac{16\times5}{8}=10\ cm$  

Example 3

• Calculate the value of h to three decimal places.

•  $\tan35\degree=\frac{h}{6}$  

•  $h=6\times\tan35\degree$  

•  $h\approx4.201$  

Multiple Choice

Which of the following is true for

$$\tan\ \theta$$  ?

• $$\frac{MN}{LM}$$  

• $$\frac{MN}{LN}$$  

• $$\frac{LM}{LN}$$  

Multiple Choice

Which of the following is true for

$$\sin\ \theta$$  ?

• $$\frac{MN}{LM}$$  

• $$\frac{MN}{LN}$$  

• $$\frac{LM}{LN}$$  

Multiple Choice

Which of the following is true for

$$\cos\ \theta$$  ?

• $$\frac{MN}{LM}$$  

• $$\frac{MN}{LN}$$  

• $$\frac{LM}{LN}$$  

Multiple Choice

What is the value of

$$\tan\ A$$  ?

• $$\frac{4}{3}$$  

• $$\frac{3}{4}$$  

• $$\frac{3}{5}$$  

• $$\frac{4}{5}$$  

Multiple Choice

What is the value of

$$\sin\ B$$  ?

• $$\frac{3}{5}$$  

• $$\frac{4}{5}$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

Multiple Choice

What is the value of

$$\cos\ B$$  ?

• $$\frac{3}{5}$$  

• $$\frac{4}{5}$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{5}$$  

Multiple Choice

Find the sin C

• 3/5

• 3/4

• 4/5

• 5/3

• 5/4

Multiple Choice

What is the length of AC if

$$\tan\ B=\frac{5}{8}$$  ?

• 5 cm

• 8 cm

• 10 cm

• 16 cm

Multiple Choice

Which of the following is correct for the diagram?

• $$\tan50\degree=\frac{h}{2.3}$$

• $$\tan50\degree=\frac{2.3}{h}$$

Multiple Choice

Which of the following equations will help you to calculate the value of p?

• $$\tan40\degree=\frac{p}{12}$$

• $$\tan40\degree=\frac{12}{p}$$

Multiple Choice

Joel calculated the value of y to be 8.3 (to 1 decimal place).

Which of these statements is true?

• Joel is correct because 20.5 × tan 22° ≈ 8.2825

• Joel is correct because 20.5 × tan 68° ≈ 8.2825

• Joel cannot be correct because the side opposite 68° must be longer than the side opposite 22°.

• Joel found the length of the hypotenuse.

Exercise/Homework

ixl.com, Algebra 1, HH.1