Question

Find the value of each variable

Answer 1

Answer:

The correct answer is option C

a = 10√3, b = 5√3, c = 15 and d = 5

Step-by-step 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

Answer 2

Answer:

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

Step-by-step explanation:

We have to find the value of each variable.

$\frac{P}{H}=sin\theta$

$\frac{b}{10}=sin 60^{\circ}$

$\frac{b}{10}=\frac}\sqrt3}{2}$

$b=10\times \frac{\sqrt3}{2}=5\sqrt3$

$\frac{d}{10}=cos 60^{\circ}$    ($cos\theta=\frac{base}{hypotenuse}$)

$d=\frac{1}{2}\times 10=5$

$\frac{b}{a}=sin30^{\circ}$

$\frac{5\sqrt3}{a}=\frac{1}{2}$

$a=10\sqrt3$

$\frac{b}{c}}=tan 30^{\circ}$   ($tan\theta=\frac{p}{b}$)

$\frac{5\sqrt3}{c}=\frac{1}{\sqrt3}$

$c=5\sqrt3\times \sqrt3=15$

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

Hence, option d is true.