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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

2. Section 4.2

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Exercise 62 Page 232

Use the cosine ratio and sine ratio to find the unknown sides.

y≈ 8.0
x≈ 7.5

Practice makes perfect

We are given the hypotenuse and an angle in a right triangle. With this information, we can use the sine ratio to find the length of the angles opposite side. We can also use the cosine ratio to find the length of the angle's adjacent side.

Let's solve for y in the first equation.

sin 47^(∘)=y/11

LHS * 11=RHS* 11

11sin 47^(∘)=y

Rearrange equation

y=11sin 47^(∘)

Use a calculator

y=8.044890...

Round to 1 decimal place(s)

y≈ 8

Let's solve for x in the second equation.

cos 47^(∘)=x/11

LHS * 11=RHS* 11

11cos 47^(∘)=x

Rearrange equation

y=11cos 47^(∘)

Use a calculator

y=7.501981...

Round to 1 decimal place(s)

y≈ 7.5

Subchapter links

4.2.1 Sine and Cosine Ratios p.232-234

4.2.2 Selecting a Trig Tool p.237-238

4.2.3 Inverse Trigonometry p.241-242

4.2.4 Trigonometric Applications p.245-247