MATHEMATICS HIGH SCHOOL

Justin was asked to write equations based on the triangle below. So far he has come up with the following equations: Which of the following would be another correct equation?

Answers

Answer 1

Answer:

C: tan 60 = √3

Step-by-step explanation:

Let the adjacent part of the triangle be x and let the opposite side be y.

Thus, from trigonometric ratios;

x/10 = cos 60

We are given cos 60 = ½

Thus;

x/10 = ½

x = ½ × 10

x = 5

Similarly;

y/10 = sin 60

Now,from trigonometric relationship we know that; sin 60 = cos 30. Thus;

y/10 = cos 30

We are given cos 30 = (√3)/2

Thus;

y/10 = (√3)/2

y = 10 × (√3)/2

y = 5√3

Since it is a right angle triangle with one angle being 60°, it means the other one is 30° since sum of angles in a triangle is 180°.

Thus;

5/(5√3) = tan 30°

1/√3 = tan 30

Similarly;

5/10 = sin 60°

sin 60° = ½

Also;

tan 60 = (5√3)/5

tan 60 = √3

Also;

sin 30 = 5/10

sin 30 = ½

Looking at the options, the only correct one is Option C

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Answers

7 to 8 i think............................

The Y is the diameter

Find Y

Area of the circle

Answers

Answer:

Y = 22.56 cm

Step-by-step explanation:

To find the diameter Y of the circle we must first find the radius of the circle

Area of a circle = πr²

where

r is the radius

From the question

Area = 400cm²

Substitute the value into the above formula and solve for the radius

That's

400 = πr²

Divide both sides by π

We have

${r}^(2) = (400)/(\pi)$

Find the square root of both sides

$r = \sqrt{ (400)/(\pi) }$

radius = 11.28 cm

Since we have the radius we can use it to find the diameter Y using the formula

diameter = radius × 2

radius = 11.28

Y = 11. 28 × 2

We have the final answer as

Y = 22.56 cm

Hope this helps you

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