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klemol [59]
3 years ago
7

If mZTUV = (9x + 1)", mZTUW = (7x-9), and mZWUV = (5x - 11)", find the value of x.

Mathematics
1 answer:
Vanyuwa [196]3 years ago
5 0

Answer:

x = 1

Step-by-step explanation:

Since, angle TUV has been divided in two parts by a ray UW

Measure of angle TUV = measure of angle TUW + measure of angle WUV

m∠TUV = m∠TUW + m∠WUV

By substituting the values of the given angles,

(9x + 1) = (7x - 9) + (5x - 11)

9x + 1 = 12x - 20

12x - 9x = 20 + 1

21x = 21

x = 1

Therefore, x = 1 will be the answer.

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Step-by-step explanation:

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Use cosine to find the missing value round to 2 decimal places #trigonometry
Naddika [18.5K]

Answer:

1. 17.27 cm

2. 19.32 cm

3. 24.07°

4. 36.87°

Step-by-step explanation:

1. Determination of the value of x.

Angle θ = 46°

Adjacent = 12 cm

Hypothenus = x

Using cosine ratio, the value of x can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos 46 = 12/x

Cross multiply

x × Cos 46 = 12

Divide both side by Cos 46

x = 12/Cos 46

x = 17.27 cm

2. Determination of the value of x.

Angle θ = 42°

Adjacent = x

Hypothenus = 26 cm

Using cosine ratio, the value of x can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos 42 = x/26

Cross multiply

x = 26 × Cos 42

x = 19.32 cm

3. Determination of angle θ

Adjacent = 21 cm

Hypothenus = 23 cm

Angle θ =?

Using cosine ratio, the value of θ can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos θ = 21/23

Take the inverse of Cos

θ = Cos¯¹(21/23)

θ = 24.07°

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Using cosine ratio, the value of θ can be obtained as follow:

Cos θ = Adjacent /Hypothenus

Cos θ = 12/15

Take the inverse of Cos

θ = Cos¯¹(12/15)

θ = 36.87°

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