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Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 3.2
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Exercise 83 Page 183

Practice makes perfect
a By the Triangle Angle Sum Theorem, the sum of a triangle's angles is 180^(∘), With this, we can write an equation.
79^(∘)+θ+90^(∘)=180^(∘) Let's solve the equation.
79+θ+90=180
AddTerms

Add terms

θ+169=180
SubEqn

LHS-169=RHS-169

θ=11
If a right triangle has an 11^(∘) angle, the ratio of this angle's opposite side to its adjacent side is 51.
Let's solve this equation.
95/x = 5/1
▼
Solve for x
DivByOne

a/1=a

95/x = 5
MultEqn

LHS * x=RHS* x

95 = 5x
DivEqn

.LHS /5.=.RHS /5.

19 = x
RearrangeEqn

Rearrange equation

x = 19
b Notice that this is a triangle with two congruent sides. Therefore, this is an isosceles triangle which means its base angles are congruent, a = b. With this, we can either replace b with a or a with b.
By the Triangle Angle Sum Theorem, the sum of a triangles three angle measures is 180^(∘). a+a+90^(∘)=180^(∘) Let's solve the equation for a.
a+a+90=180
AddTerms

Add terms

2a+90=180
SubEqn

LHS-90=RHS-90

2a=90
DivEqn

.LHS /2.=.RHS /2.

a=45
Both a and b are 45^(∘).
c If a right triangle has a 22^(∘) angle, the ratio of this angles opposite side to its adjacent side is 25.
Let's solve this equation.
70/y = 2/5
▼
Solve for y
MultEqn

LHS * y=RHS* y

70 = 2/5* y
MultEqn

LHS * 5=RHS* 5

350 = 2y
DivEqn

.LHS /2.=.RHS /2.

175 = y
RearrangeEqn

Rearrange equation

y = 175
Subchapter links expand_more
arrow_right 3.2.1 Constant Ratios in Right Triangles p.178-180
72
Constant Ratios in Right Triangles 73 (Page 179)
Constant Ratios in Right Triangles 74 (Page 179)
Constant Ratios in Right Triangles 75 (Page 179)
Constant Ratios in Right Triangles 76 (Page 179)
Constant Ratios in Right Triangles 77 (Page 180)
arrow_right 3.2.2 Connecting Slope Ratios to Specific Angles p.183-184
Connecting Slope Ratios to Specific Angles 83 (Page 183)
Connecting Slope Ratios to Specific Angles 84 (Page 184)
Connecting Slope Ratios to Specific Angles 85 (Page 184)
Connecting Slope Ratios to Specific Angles 86 (Page 184)
Connecting Slope Ratios to Specific Angles 87 (Page 184)
Connecting Slope Ratios to Specific Angles 88 (Page 184)
arrow_right 3.2.3 Expanding the Trig Table p.187-188
Expanding the Trig Table 93 (Page 187)
Expanding the Trig Table 94 (Page 187)
Expanding the Trig Table 95 (Page 187)
Expanding the Trig Table 96 (Page 188)
Expanding the Trig Table 97 (Page 188)
Expanding the Trig Table 98 (Page 188)
arrow_right 3.2.4 Expanding the Trig Table p.192-193
Expanding the Trig Table 105 (Page 192)
Expanding the Trig Table 106 (Page 192)
Expanding the Trig Table 107 (Page 192)
Expanding the Trig Table 108 (Page 192)
Expanding the Trig Table 109 (Page 193)
Expanding the Trig Table 110 (Page 193)
arrow_right 3.2.5 Applying the Tangent Ratio p.195-196
Applying the Tangent Ratio 113 (Page 195)
Applying the Tangent Ratio 114 (Page 196)
Applying the Tangent Ratio 115 (Page 196)
Applying the Tangent Ratio 116 (Page 196)
Applying the Tangent Ratio 117 (Page 196)
Applying the Tangent Ratio 118 (Page 196)