Question

What are the exact values of a and b

Answer 1

Answer:

• a = 5
• b = 5√3

Step-by-step explanation:

We can find the values of a and b using the Trigonometric Identities:

$\boxed{sin\theta=\frac{opposite}{hypotenuse}}$

$\boxed{cos\theta=\frac{adjacent}{hypotenuse} }$

$\boxed{tan\theta=\frac{opposite}{adjacent} }$

Given:

• θ = 30°
• hypotenuse = AB = 10
• opposite = BC = a
• adjacent = AC = b

$\displaystyle sin\theta=\frac{opposite}{hypotenuse}$

$\displaystyle sin(30^o)=\frac{a}{10}$

$a=10\times sin(30^o)$

$a=10\times\frac{1}{2}$

$\bf a=5$

$\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$

$\displaystyle cos(30^o)=\frac{b}{10}$

$b=10\times cos(30^o)$

$b=10\times\frac{1}{2}\sqrt{3}$

$\bf b=5\sqrt{3}$

Answer 2

Answer:

The value of a and b in the figure are 5 and 5√3.

Step-by-step explanation:

We have

From the figure,

Sin 30 = a/10

Cos 30 = b/10

Now,

Sin 30 = 1/2

Cos 30 = √3/2

Now,

1/2 = a/10

a = 5

√3/2 = b/10

b = 5√3

Thus,

The value of a and b are 5 and 5√3.