Question

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse? Check all that apply.
A. 2: 3 sqrt 3
B. sqrt 2: sqrt 3
C. sqrt 3: 2
D: 1: sqrt 2
E: 3: 1 sqrt 2
F: 2: 2 sqrt 2

Answer 1

Answer:

Option C is correct.

Ratio of longer leg to hypotenuse is;  $\sqrt{3} : 2$

Step-by-step explanation:

This is the special right angle triangle 30°-60°-90°  as shown below in the figure.

• The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.

• The side opposite the 60° angle will be the longer leg, because 60 degrees is the mid-sized degree angle in this triangle.

• Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.

In 30°−60°−90° right triangle,

• the length of the hypotenuse is twice the length of the shorter leg,also
• the length of the longer leg is $\sqrt{3}$ times the length of the shorter leg.

Then:

the sides are in proportion i.e,  $1:\sqrt{3} :2$

Therefore, the ratio of the length of the longer leg to the length of its hypotenuse is:  $\sqrt{3} : 2$

Answer 2

Answer:  The answer is (C) $\sqrt3:2.$

Step-by-step explanation: As given in the question, a right-angled triangle ABC is drawn in the attached figure, where

∠A = 30°, ∠B = 90° and ∠C = 60°.

The longest leg is AB, AC is the hypotenuse and BC is the shortest leg.

To find :- AB : AC.

We have from the right-angled triangle ABC,

$\dfrac{AB}{AC}=\dfrac{p}{h}=\sin 60^\circ\\\\\Rightarrow AB:AC=\dfrac{\sqrt3}{2}\\\\\Rightarrow AB:AC=\sqrt3:2.$

Thus, the correct option is (C).