Question

Matttttttttthhhhhhhhh

Answer 1

Answer: B 9

Explanation:

This is a 30-60-90 triangle and follows a ratio rule.

short leg = x = a

hypotenuse = 2x = 2a

long leg = x√3 = a√3

Given:

a=3√3

Find: b

solution:

b is long leg:

long leg = x√3 = a√3

b = a√3

b = 3√3 *√3

b= 3*3

b=9

Answer 2

b = 9

Explanation:

The given right triangle is a special type of triangle called a 30-60-90 triangle, as its interior angles are 30°, 60° and 90°.

The sides of a 30-60-90 triangle are in the ratio 1 : √3 : 2.

Therefore, the formula for the ratio of the sides is x : x√3 : 2x where:

• x is the shortest side opposite the 30° angle.
• x√3 is the side opposite the 60° angle.
• 2x is the longest side (hypotenuse) opposite the right angle.

From observation of the given diagram, we can see that side a is opposite the 30° angle. Given that a = 3√3, then x = 3√3.

Side b is opposite the 60° angle.

Therefore, to find the value of b, substitute x = 3√3 into the expression for the side opposite the 60° angle:

`\begin{aligned}\implies b&=x√(3)\\&=3 √(3) \cdot √(3)\\&=3 \cdot 3\\&=9\end{aligned}`

Therefore, the value of b is 9.