# why did the professional dog walker go out of business answer key

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## Why did the professional dog walker go out of business math worksheet answers?

Why Did the Professional Dog Walker ao Out of business, math worksheet Answers:

**Q1. sin27° = x/8
**

Solution:

We have to solve for x, therefore, we will rearrange the given equation for x.

We get,

x = 8 × sin27°

Using the calculator,

sin27° = 0.45

Now substitute the value of sin27° into the main equation.

we get,

x = 8 × 0.45

**x = 3.63 (rounded to the nearest hundredth)**

**Q2. tan 18° = n / 75**

Solution:

We have to solve for n, therefore, we will rearrange the given equation for n.

We get,

n = 75 × tan 18°

Using the calculator,

tan 18° = 0.32

Now substitute the value of **tan 18°** into the main equation.

we get,

x = 75 × 0.32

**x = 24.37 (rounded to the nearest hundredth)**

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**Q3. sin40° = 4 / a**

Solution: We have to solve for a, therefore, we will rearrange the given equation for a.

We get,

a = 4 ÷ sin40°

Using the calculator,

sin40° = 0.64

Now substitute the value of sin40° into the main equation.

we get,

a = 4 ÷ 0.64

**a = 6.25 (rounded to the nearest hundredth)
**

**Q4. cos5° = 92 / y**

Solution: We have to solve for y, therefore, we will rearrange the given equation for y.

We get,

y = 92 ÷ cos5°

Using the calculator,

Cos5° = 0.99

Now substitute the value of cos5° into the main equation.

we get,

y = 92 ÷ 0.99

**y = 92.92 (rounded to the nearest hundredth)
**

**
Q5:** Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 35°

length of Opposite side to the angle = x

Length of Hypoteneus = 12

Calculations:

Using the SOH CAH TOA rules:

SOH stands for SineФ = Opposite ÷ Hypotenuse.

CAH stands for CosineФ = Adjacent ÷ Hypotenuse.

TOA stands for TangentФ = Opposite ÷ Adjacent.

Hence,

SineФ = Opposite ÷ Hypotenuse

Substituting the values:

Sine35° = x ÷ 12

0.5735 = x ÷ 12

x = 0.5735 × 12

**x = 6.88 (rounded to the nearest hundredth)**

**Q6: **Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 54°

length of the adjacent side to the angle = x

Length of Hypoteneus = 30

Calculations:

Using the SOH CAH TOA rules:

Hence,

CosineФ = Adjacent ÷ Hypotenuse

Substituting the values:

Cos54° = x ÷ 30

0.5877 = x ÷ 30

x = 0.5877 × 30

**x = 17.63 (rounded to the nearest hundredth)**

**Q7: **Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 22°

length of the adjacent side to the angle = 85

length of the opposite side to the angle = x

Calculations:

Using the SOH CAH TOA rules:

Hence,

TangentФ = Opposite ÷ Adjacent

Substituting the values:

tan22° = x ÷ 85

0.4040 = x ÷ 85

x = 0.4040 × 85

**x = 34.34 (rounded to the nearest hundredth)**

**Q8: **Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 16°

length of the opposite side to the angle = x

Length of Hypoteneus = 14

Calculations:

Using the SOH CAH TOA rules:

Hence,

CosineФ = Adjacent ÷ Hypotenuse

Substituting the values:

Sine16° = x ÷ 14

0.2756 = x ÷ 14

x = 0.2756 × 14

**x = 3.86 (rounded to the nearest hundredth)**

**Q9: **Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 65°

length of the adjacent side to the angle = 9

length of the opposite side to the angle = x

Calculations:

Using the SOH CAH TOA rules:

Hence,

TangentФ = Opposite ÷ Adjacent

Substituting the values:

tan65° = x ÷ 9

2.1445 = x ÷ 9

x = 2.1445 × 9

**x = 19.30 (rounded to the nearest hundredth)**

**Q10: **Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 51°

length of the adjacent side to the angle = x

Length of Hypoteneus = 70

Calculations:

Using the SOH CAH TOA rules:

Hence,

CosineФ = Adjacent ÷ Hypotenuse

Substituting the values:

Cos51° = x ÷ 70

0.6293 = x ÷ 70

x = 0.6293 × 70

**x = 44.05 (rounded to the nearest hundredth)**

**Q11: **Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 36°

length of the opposite side to the angle = 15

Length of Hypoteneus = x

Calculations:

Using the SOH CAH TOA rules:

Hence,

CosineФ = Adjacent ÷ Hypotenuse

Substituting the values:

Sine36° = 15 ÷ x

0.5877 = 15 ÷ x

x = 15 ÷ 0.5877

**x = 25.52 (rounded to the nearest hundredth)**

**Q12: **Given the shape attached, therefore, using the triangle given, we have:

Angle of elevation = 60°

length of the adjacent side to the angle = x

length of the opposite side to the angle = 100

Calculations:

Using the SOH CAH TOA rules:

Hence,

TangentФ = Opposite ÷ Adjacent

Substituting the values:

tan65° = 100 ÷ x

2.1445 = 100 ÷ x

x = 100 ÷ 2.1445

**x = 46.63 (rounded to the nearest hundredth)**

**Q13:** When a 25-ft ladder is leaned against a wall, it makes a 72° with the ground. How high up on wall does the ladder reach?

**Solution: **Given the shape attached, therefore, using the triangle given, we have:

The angle of elevation from the ground = 72°

length of the wall opposite to the angle = X

Length of ladder (Hypoteneus) = 25 feet

Calculations:

Using the SOH CAH TOA rules:

Hence,

SineФ = Opposite ÷ Hypotenuse

Substituting the values:

Sine72° = x ÷ 25

0.9510 = x ÷ 25

x = 25 ÷ 0.9510

**x = 23.77 (rounded to the nearest hundredth)**

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