Given PQR ~ STR, find QT

Given △DEF, which is not equal to cos(F)? sin(F). sin(D). tan(F). cos(D)

valentina_108 [34]

Answer: The correct option is tan(F).

Explanation:

In the given figure the triangle is a right angle triangle because $\angle E=90^{\circ}$ .

It is also given that $DE=EF=5$ and $DF=5\sqrt{2}$ .

Since it is an isosceles right angle triangle, therefore the value of perpendicular and base is same for both angles D and F, which is 5.

$\cos (F)=\frac{Base}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of cos(F) is $\frac{1}{\sqrt{2}}$ .

$\sin (F)=\frac{Perpendicular}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of sin(F) is $\frac{1}{\sqrt{2}}$ .

$\sin (D)=\frac{Perpendicular}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of sin(D) is $\frac{1}{\sqrt{2}}$ .

$\tan (F)=\frac{Perpendicular}{Base}=\frac{5}{5} =1$

The value of tan(F) is 1. Which is not equal to $\frac{1}{\sqrt{2}}$ .

$\cos (D)=\frac{Base}{Hypotenuse} =\frac{5}{5\sqrt{2}} =\frac{1}{\sqrt{2}}$

The value of cos(D) is $\frac{1}{\sqrt{2}}$ .

Therefore, the value of tan(F) is not equal to the value of cos(F), so the correct option is third.

3 0

2 years ago

Read 2 more answers

Which of the following gives all of the sets that contain -1/2?

fiasKO [112]

ANSWER

The set of all rational numbers and the set of all real numbers.

EXPLANATION

The set of rational numbers contains all numbers that can be written in the form,

$\frac{a}{b}$

where a and b are integers and b≠0.

The given number is

$- \frac{1}{2}$

It belongs to the set of rational numbers.

The set of rational numbers is a subset of the set of real numbers.

Hence

$- \frac{1}{2}$
also belongs to the set of real numbers.

The correct answer is A.

3 0

2 years ago

One month julia collected 8.4 gallons of rainwater. That month she used 5.2 gallons of rainwater to water her garden and 6.5 gal

Andru [333]

Given

One month julia collected 8.4 gallons of rainwater.

she used 5.2 gallons of rainwater to water her garden

6.5 gallons of rainwater to water flowers

Find out how much was the supply of rainwater increased or decreased by the end of the month.

To proof

As given in the question

One month julia collected 8.4 gallons of rainwater

she used 5.2 gallons of rainwater to water her garden and 6.5 gallons of rainwater to water flowers

Total water she used in the month = 5.2 gallons + 6.5gallons

= 11.7 gallons

Let the supply of rainwater increased or decreased by the end of the month

be x .

Than the equation become in the form

x + 8.4 = 11.7

x = 3.3 gallons

Therefore the supply of rainwater increased or decreased by the end of the month is 3.3 gallons.

Hence proved

8 0

2 years ago

Read 2 more answers

In 2008, the price of a gallon of unleaded gasoline was $4.02. In 1990, it was only $1.37 per gallon. What is the increase expre

liubo4ka [24]

First get the difference between the 2008 price and 1990 which is $4.02-$1.37= $2.65. Then the difference you've got which is $2.65, divide it to the current market price which is $4.02 to get the how many percentage it increased since then, $2.65/$4.02= 0.65920398 then multiply it to 100. It would be 65.92 or 66% if rounded off to whole number.

6 0

2 years ago

In circle O, what is m∠MAJ?

ira [324]

we know that

The measure of the interior angle is the half-sum of the arcs comprising it and its opposite.

so

Find the measure of the angle LAM

m∠LAM is equal to

$\frac{1}{2}*[arc\ KJ+arc\ LM]= \frac{1}{2}*[170+80]\\\\=125\ degrees$