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2 years ago

In the triangle below, what is the length of the side opposite the 30 degree angle

Mathematics

1 answer:

victus00 [196]2 years ago

6 0

Answer:

The correct answer is option A. √3

Step-by-step explanation:

From the figure we can see that aright angled triangle.

Points to remember

If a right angled triangle with angle 30°, 60° and 90° then the sides are in the ratio, 1 : √3 : 2

<u>To find the length of side opposite to 30°</u>

Let 'x' be the side opposite to the 30°, the we can write,

x : 3 : Hypotenuse = 1 : √3 : 2

Therefore x = 3/√3 = √3

The length of side opposite to the 30° is √3

The correct answer is option A. √3

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What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

GalinKa [24]

Options

A. UV = 14 ft and m∠TUV = 45°

B. TU = 26 ft

C. m∠STU = 37° and m∠VTU = 37°

D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°

E. m∠UST = 98° and m ∠TUV = 45°

Answer:

A. UV = 14 ft and m∠TUV = 45°

D. ST = 20 ft, UV = 14 ft, and m∠UST = 98°

Step-by-step explanation:

Given

See attachment for triangle

Required

What proves that: ΔSTU ≅ ΔVTU using SAS

To prove their similarity, we must check the corresponding sides and angles of both triangles

First:

$\angle UST$ must equal $\angle UVT$

So:

$\angle UST = \angle UVT = 98$

Next:

UV must equal US.

So:

$UV = US = 14$

Also:

ST must equal VT

So:

$ST = VT = 20$

Lastly

$\angle TUV$ must equal $\angle TUS$

So:

$\angle TUV = \angle TUS = 45$

Hence: Options A and D are correct

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