Question

Question 6 and 7 explain and solve

Answer 1

• 6. x = 7ft
• 7. θ = 60°

Explanation:

For question no. 6

In ΔXYZ with respect to ∡X = 51°

Opposite = YZ = x

Base = XZ = y

Hypotenuse = XY = 9 ft

Using Trigonometric ratio of which gives relation among angle, opposite and opposite is given by sine. So,

`\tt Sin X = ( Opposite )/( Hypotenuse) = (YZ)/(XY)`

substituting value

`\tt Sin (51) = (x)/(9)`

Doing crisscross multiplication, we het

`\tt Sin(51)*9 = x`

x=6.99 in nearest value

x = 7 ft

Therefore, The value of x is 7 ft

`\hrulefill`

For question no. 7

In ΔXYZ with respect to ∡A = θ

Opposite = BC = a

Base = AC = 5 cm

Hypotenuse = AB = 10 cm

Using Trigonometric ratio of which gives relation among angle, base and opposite is given by cosine, So,

`\tt Cos A = ( Base )/( Hypotenuse) = (AC)/(AB)`

substituting value

`\tt Cos A = (5)/(10)`

`\tt Cos A = (1)/(2)`

Since Angle A (θ) =
`\tt ArcCos ((1)/(2)) \:or\: Cos^(-1)((1)/(2))`

Therefore, Angle A (θ) = 60°