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 ___________.

A. 5, 5√3
B. 20√3,5
C. 10√3, 10√3
D. 5,√2, 5√2
E. 5, 10√3
F. 10√3,20

(Picture below.)

Answer 1

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=\frac{\textup{base}}{\textup{hypotenuse}}\\\\\\\Rightarrow (1)/(2)=(s)/(10)\\\\\\\Rightarrow s=(10)/(2)\\\\\\\Rightarrow s=5,`

and

`\sin 60^\circ=\frac{\textup{perpendicular}}{\textup{hypotenuse}}\\\\\\\Rightarrow (\sqrt3)/(2)=(q)/(10)\\\\\\\Rightarrow q=(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.

Answer 2

A. 5, 5√3

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.