Question

Find the value of each variable

Answer 1

d.
`a=10\sqrt3,b=5\sqrt3,c=15,d=5`

Explanation:

We have to find the value of each variable.

`(P)/(H)=sin\theta`

`(b)/(10)=sin 60^(\circ)`

`(b)/(10)=\frac}\sqrt3}{2}`

`b=10* (\sqrt3)/(2)=5\sqrt3`

`(d)/(10)=cos 60^(\circ)` (
`cos\theta=(base)/(hypotenuse)`)

`d=(1)/(2)* 10=5`

`(b)/(a)=sin30^(\circ)`

`(5\sqrt3)/(a)=(1)/(2)`

`a=10\sqrt3`

`(b)/(c)}=tan 30^(\circ)` (
`tan\theta=(p)/(b)`)

`(5\sqrt3)/(c)=(1)/(\sqrt3)`

`c=5\sqrt3* \sqrt3=15`

`a=10\sqrt3,b=5\sqrt3,c=15,d=5`

Hence, option d is true.

Answer 2

The correct answer is option C

a = 10√3, b = 5√3, c = 15 and d = 5

Explanation:

Points to remember

The angles of a right angled triangle, 30°, 60° and 90° then sides are in the ratio, 1: √3 : 2

To find the value of variables

From the figure we can see 2 right angled triangle with angle 30, 60 and 90

we get, d= 5 then b = 5√3

b = 5√3 the c = 5√3 * √3 = 15

and a = 2 * 5√3 = 10√3

Therefore the correct answer is option C

a = 10√3, b = 5√3, c = 15 and d = 5