Question

Fill in the blanks. In the 30-60-90 triangle below, side s has a length of ___________ and side q has a length of ___________.

Answer 1

Answer:

A. 5, 5√3

Step-by-step explanation:

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

Given: 2x = 10 [From the figure]

x = 10/2

x = 5.

Therefore, s =5 and q = √3x

q = 5√3

Answer: A. 5, 5√3

Hope this will helpful.

Thank you.

Answer 2

Answer:  The correct option is (A)  5, 5√3.

Step-by-step explanation:  We are given a 30-60-90 triangle, where the length of the hypotenuse is 10 units.

We are to find the length of sides s and q.

We have, using trigonometric ratios in the given right-angles triangle that

$\cos 60^\circ=\dfrac{\textup{base}}{\textup{hypotenuse}}\\\\\\\Rightarrow \dfrac{1}{2}=\dfrac{s}{10}\\\\\\\Rightarrow s=\dfrac{10}{2}\\\\\\\Rightarrow s=5,$

and

$\sin 60^\circ=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}\\\\\\\Rightarrow \dfrac{\sqrt3}{2}=\dfrac{q}{10}\\\\\\\Rightarrow q=\dfrac{10\sqrt3}{2}\\\\\\\Rightarrow q=5\sqrt3.$

Therefore, s = 5 units  and  q = 5√3 units.

Thus, the complete statement is

In the given 30-60-90 triangle, side s has a length of 5 units and side q has a length of 5√3 units.