Question

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Give the Answer in Attachment.


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Answer 1

Answer:

By trigonometry we know that :

sin theta = ( side opposite to theta ) / ( longest side )

Hence we can write that :

sin 40 = y / 10

sin 40 = 0.641 [ approx ]

⇒ 0.643 = y/10

⇒ y = 0.643 × 10

⇒ y ≈ 6.43 km .

Now we know that by Pythagoras theorem :

x² + y² = 10²

⇒ x² + ( 6.43 )² = 100

⇒ x² = 100 - 41.345

⇒ x² = 58.655

⇒ x ≈ 7.66 km

Step-by-step explanation:

The Pythagoras theorem states :

( longest side )² = ( base )² + ( height )²

The theorem is applied in right angles .

Here sin 40 is used but it is an approximate value only .

Answer 2

ANSWER

1)y = 6.4279 km.

2)x = 7.6604 km.

Step By Step Explanation

Plz, refer to the attachment for the diagram.

In the given diagram we have =>

Angle A = 40°.

Angle C = 50°.

Length of CB = y km.

length of AC = 10 km.

length of AB = x km.

Now by using trigonometric ratios, we have =>

Sin A = $\dfrac{Perpendicular}{Hypotenuse}$

=>Sin 40° = $\dfrac{y}{10}$

=>0.64279(approx.) = $\dfrac{y}{10}$

=> y = 0.64279 × 10

=> y = 6.4279 km. (approx. value)

Now we have =>

Sin C = $\dfrac{Perpendicular}{Hypotenuse}$

=>Sin 50° = $\dfrac{x}{10}$

=>0.76604(approx.) = $\dfrac{x}{10}$

=> x = 0.76604 × 10

=>x = 7.6604 km. (approx. value)

REMEMBER

-The trigonometric ratio table is very important to be remembered.

-Also, remember =>

1)Sin A = $\dfrac{Perpendicular}{Hypotenuse}$

2)Cos A = $\dfrac{Base}{Hypotenuse}$

3)Tan A = $\dfrac{Perpendicular}{Base}$

4)Sin A = $\dfrac{1}{Cosec A}$

5)Cos A = $\dfrac{1}{Sec A}$

6)Tan A = $\dfrac{1}{Cot A}$