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Vadim26 [7]
3 years ago
14

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 to the length of its hypotenuse? CHECK A

LL THAT APPLY.
A. √3 : 2
B. 3 : 2√3
C. 1 : √3
D. 3√3 : 6
E. √3 : √3
F. √2 : √3

-Apex Learning, Geometry
Mathematics
1 answer:
8_murik_8 [283]3 years ago
4 0

Answer:

A. √3 : 2

D. 3√3 : 6

Step-by-step explanation:

In a triangle described as 30°-60°-90° triangle, the base angles are 90° and 60°

The side with angles 90° and 60° is the shortest leg and can be represented by 1 unit

The hypotenuse side is assigned a value twice the shorter leg value, which is 2 units

From Pythagorean relationship; the square of the hypotenuse side subtract the square of the shorter leg gives the square of the longer side

This is to say if;

The given the shorter leg = 1 unit

The hypotenuse is twice the shorter leg= 2 units

The longer leg is square-root of the difference between the square of the hypotenuse and that of the shorter leg

=2^2-1^2\\\\=4-1=3\\\\\\b^2=3\\\\\\b=\sqrt{3}

where the longer leg is represented by side b in the Pythagorean theorem, the hypotenuse by c and the shorter leg by a to make;

a^2+b^2=c^2

<u>Hence the summary is</u>

a=shorter leg= 1 unit

b=longer leg = √3 units

c=hypotenuse=2 units

The ratio of longer leg to its hypotenuse is

=√3:2⇒ answer option A

This is the same as 3√3:6 ⇒answer option D because you can divide both sides of the ratio expression by 3 and get option A

=3\sqrt{3} :6\\\\\\\frac{3\sqrt{3} }{3} :\frac{6}{3} \\\\\\=\sqrt{3} :2

Answers are :option A and D

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<em><u>Given </u></em><em><u>-</u></em>

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Step-by-step explanation:

Remark

Use the Pythagorean theory to find the height. Use that height to find the area of the rectangle and the triangle Or

You can find the area of the trapezoid which requires only 1 step after you find the height.

Height

c = 8

b = 4

a = ?

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