Question

A 30-meter antenna mast is stabilized by a 34 meter guy wire. How far from the base of the mast is the guy wire secured to the ground

A. 32 m
B. 64 m
C. 16 m
D. 4 m

Answer 1

Hello!

The answer is: C. 16 m.

Why?

The figure is a right triangle, it means that we can solve it by using the Pythagorean theorem which states that, the largest side of a rectangle (hypotenuse) is equal to the sum of the other two side squares:

$c^{2} =a^{2} + b^{2}$

Where:

c=34m

a=30m

b=?

So, by substituting we have:

$34^{2}=a^{2} +30^{2} \\a=\sqrt{34^{2-}30^{2}}=16$

Have a nice day!

Answer 2

Answer:

The correct answer is option C. 16 m

Step-by-step explanation:

Pythagoras theorem:

Hypotenuse² = Base² + Height²

It is given that,A 30-meter antenna mast is stabilized by a 34 meter guy wire.

From the figure we can see a right angled triangle.

Hypotenuse = 34 m

Height = 30

To find distance

We have to find the base of right angled triangle

Hypotenuse² = Base² + Height²

Base² = Hypotenuse² - Height²

  = 34² - 30² = 1156 - 900

  = 256

Base = √256 = 16 m

Therefore distance from the base of the mast is the guy wire secured to the ground = 16 m

The correct answer is option C. 16 m