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KatRina [158]
3 years ago
6

Troy is building a rectangular garden that is 10 feet by 6 feet.What should be the length of the diagonals to ensure a 90 degree

angle?
Mathematics
2 answers:
qaws [65]3 years ago
4 0

Answer:

Length of the diagonals = 11.66 feet

Step-by-step explanation:

Troy is building a rectangular garden with dimensions 10 feet and 6 feet.

We have to calculate the length of the diagonals of the park to ensure a 90° angle.

As we know in a rectangle all angles are of 90° and both the diagonals are of same length.

Therefore by Pythagoras theorem we can find the diagonal of the rectangle.

Diagonal² = 10² + 6²

Diagonal = √(100+36) = √(136)

               = 11.66 feet

Therefore, length of the diagonals will be = 11.66 feet

mina [271]3 years ago
3 0
6^2 + 10^2 equals 11.67
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The value of tangent theta is equal to the negative 1.  At this value the value of secant theta is \sqrt{2}.

<h3>What is tangent theta?</h3>

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

\rm tan\theta=\dfrac{sin \theta}{cos \theta}

Given information-

The value of tangent theta is equal to the negative 1.

\tan \theta=-1

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

\rm tan\theta=\dfrac{sin \theta}{cos \theta}

The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,

\rm -1=\dfrac{sin \theta}{cos \theta}\\

Simplify it further as,

\rm -cos \theta=sin \theta

When the value of cosine and sine theta is equal, then the angle exist in 4th quadrant with the value of \dfrac{7\pi}{4}. Which extent to the \sqrt{2}/2 for the cosine function.

In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,

\rm \dfrac{1}{sec\theta}=\dfrac{\sqrt{2}}{2}\\sec\theta=\sqrt{2}

Thus the value of secant theta is \sqrt{2}

Learn more about the tangent theta here;

brainly.com/question/29190

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