In circle D, which is a secant? <br> A. EF<br> B. DC<br> C. AB<br> D. GH

What is the value of tan(60°)? One-half StartRoot 3 EndRoot StartFraction StartRoot 3 EndRoot Over 2 EndFraction StartFraction 1

Ratling [72]

Answer:

$\sqrt3$

Step-by-step explanation:

To find:

The value of $tan60^\circ$ = ?

Solution:

Kindly consider the equilateral $\triangle ABC$ as attached in the answer area.

Let the side of triangle = $a$ units

Let us draw the perpendicular from vertex A to side BC.

It will divide the side BC in two equal parts.

i.e. BD = DC = $\frac{a}{2}$

Using Pythagorean Theorem in $\triangle ABD$ :

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}$

Side AD = $\frac{\sqrt3}{2}a$

Using Trigonometric ratio:

$tan\theta = \dfrac{Perpendicular}{Base}$

$tanB = \dfrac{AD}{BD}$

Putting the values of AD and BD:

$tan60^\circ=\dfrac{\frac{\sqrt3}{2}a}{\frac{1}{2}a}\\\Rightarrow tan60^\circ = \bold{\sqrt3}$

5 0

2 years ago

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From the top of a 100-ft building a man

romanna [79]

Answer:

219m

Step-by-step explanation:

Since the man observes the car with angle 15 before observing in 33 degrees.

For the first observation

The angle observation gives an angle if 33 degrees with the horizontal.

It gives a triangle which I'll attach to the que,

from the first triangle

Tan 33 = 100/y

Y= 100/ tan 33

Y = 153.99m.

This is the distance from the building to the distance where it was secondly observed( 33).

To find x

tan 15 = 100/(153.99+x)

153.99 + x = 100/ tan 15

153.99 + x = 373.21

The distance between the two observed angles

X= 219m.

5 0

3 years ago

Write an equation for (-1,-2),(-3,-4)

Marina86 [1]

Answer:

y=x+1

Step-by-step explanation:

First find the slope by subtracting the y values from both points and dividing it by the subtraction of the x values from both points:

-4--2/ -3--1= -2/-2= 1

so the slope is 1

Now find the y-intercept by plugging in the x and y from one of the points into the equation y=x+b

-3=-4+b

1=b

now plug the slope and y intercept in:

y=x+1

hope this helps :D

7 0

3 years ago

The new number, 550, is 200 more than the original number. What is the approximate percent change?a The percent change is 33%. b

Svetradugi [14.3K]

B The percentage change is 55%

8 0

3 years ago

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13.......................

Alla [95]

Answer:

The answer is (d) ⇒ $pq^{2}r\sqrt[3]{pr^{2}}$

Step-by-step explanation:

* To simplify the cube roots:

If its number then the number must be written in the form x³

then we divide the power by 3 to cancel the radical

If its variable we divide its power by 3 to cancel the radical

∵ $\sqrt[3]{p^{4}q^{6}r^{5}}=p^{\frac{4}{3}}q^{\frac{6}{3}}r^{\frac{5}{3}}}$

∴ $p^{\frac{4}{3}}q^{2}}r^{\frac{5}{3}}=p^{1\frac{1}{3}}q^{2}r^{1\frac{2}{3}}$

∵ $p^{\frac{1}{3}}=\sqrt[3]{p}$

∵ $r^{\frac{2}{3}}=\sqrt[3]{r^{2}}$

∴ $p(p)^{\frac{1}{3}}q^{2}r(r)^{\frac{2}{3}}=p(\sqrt[3]{p})q^{2}r(\sqrt[3]{r^{2}})$

∴ $prq^{2}\sqrt[3]{pr^{2}}}$

∴ The answer is (d)

5 0

2 years ago

In circle D, which is a secant? A. EF B. DC C. AB D. GH