body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Core Connections Integrated II, 2015

CC

Core Connections Integrated II, 2015 View details

2. Section 3.2

Continue to next subchapter

Exercise 105 Page 192

Practice makes perfect

a We want to find the missing side, and to do so we have to use the tangent ratio. This is because we have been given the reference angle's adjacent side and want to find the length of its opposite side.

tan θ =opposite/adjacent

By substituting the measures of the reference angle and side lengths in this formula, we can write an equation describing the length of the opposite side, t.

Let's solve for t in our equation.

tan 8^(∘)=t/82

▼

Solve for t

LHS * 82=RHS* 82

82tan 8^(∘)=t

Rearrange equation

t=82tan 8^(∘)

Use a calculator

t=11.52434...

Round to 1 decimal place(s)

t≈ 11.5

The side labeled t is 11.5 units.

b Like in Part A, we can use the tangent ratio. However, in this case we want to determine the reference angle's adjacent side.

Let's solve for p in our equation.

tan 75^(∘)=12/p

▼

Solve for p

LHS * p=RHS* p

tan 75^(∘)* p=12

.LHS /tan 75^(∘).=.RHS /tan 75^(∘).

p=12/tan 75^(∘)

Use a calculator

p=3.21539...

Round to 1 decimal place(s)

p≈ 3.2

The side labeled p is 3.2 units.

c Like in Parts A and B, we can solve for the unknown leg by using the tangent ratio.

Let's solve for b in our equation.

tan 68^(∘)=b/60

▼

Solve for b

LHS * 60=RHS* 60

60tan 68^(∘)=b

Rearrange equation

b=60tan 68^(∘)

Use a calculator

b=48.50521...

Round to 1 decimal place(s)

b≈ 48.5

The side labeled b is 48.5 units.

Subchapter links

3.2.1 Constant Ratios in Right Triangles p.178-180

3.2.2 Connecting Slope Ratios to Specific Angles p.183-184

3.2.3 Expanding the Trig Table p.187-188

3.2.4 Expanding the Trig Table p.192-193

3.2.5 Applying the Tangent Ratio p.195-196