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3 years ago

Evaluate:cos 45°/sec 30°+cosec30°

Mathematics

1 answer:

barxatty [35]3 years ago

3 0

Look at the trigonometry table for special angles.

From here, substitute the values in:

$\frac{\sqrt{2} }{2} / \frac{2\sqrt{3} }{3}} + 2$

Simplify:

$\frac{3\sqrt{2} }{4\sqrt{3} } + 2$

Rationalize:

$\frac{\sqrt{6} }{4} +2$

And this is your answer.

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Which equation could be used to find the height of the flagpole

Sauron [17]

X = height of pole (in meters)

With respect to the 50 degree angle, the side x is the opposite leg. It is the leg furthest from the reference angle. The hypotenuse is 5 meters.

The trig function sine ties together the opposite and hypotenuse

sin(angle) = opposite/hypotenuse
sin(50) = x/5
5*sin(50) = x .... multiply both sides by 5
x = 5*sin(50)

------------------

Since x = 5*sin(50) isn't listed as an answer choice, let's try using cosine. We can't use it right away because we don't know the adjacent side. What we can do is change the reference angle. The missing angle of the triangle is 90-50 = 40 degrees. Let's make the 40 degree angle the reference angle

So x is now the adjacent side with respect to the 40 degree reference angle. The hypotenuse is always the longest side. The hypotenuse stays at 5.

cos(angle) = adjacent/hypotenuse
cos(40) = x/5
5*cos(40) = x
x = 5*cos(40)

This expression is listed. The answer is choice B

4 0

3 years ago

A lamp post with a height of 12 ft casts a shadow of 6 ft. A fire hydrant near it casts a shadow that is 1.5 ft long. How tall i

alex41 [277]

Answer:

3ft

Step-by-step explanation:

We are given that

Height of lamp, h=12ft

Height of shadow, l=6ft

Height of shadow of hydrant, l'=1.5ft

Let height of hydrant=h'

We have to find the height of fire hydrant.

All right triangles are similar

When two triangles are similar then, the ratio of their corresponding sides are equal.

Using the property

$\frac{h}{h'}=\frac{l}{l'}$

$\frac{12}{h'}=\frac{6}{1.5}$

$h'=\frac{12\times 1.5}{6}$

$h'=3$ ft

Hence, the height of fire hydrant=3 ft

3 0

3 years ago

Answers+steps please?

koban [17]

A) 40 feet
B) 1 second
C) 56 feet

3 0

3 years ago

What is the greatest common factor of 16 and 48?

Anna11 [10]

Answer:

Step-by-step explanation:

We can list out each of the numbers' prime factors first before deciding their greatest common factor.

16: 2 × 2 × 2 × 2

48: 2 × 2 × 2 × 2 × 3

As you can see the bolded parts, these are the common factors of the two numbers. To find the greatest common factors, we just have to multiply all their common factors together.

Greatest common factor of 16 & 48: 2 × 2 × 2 × 2 = 16

7 0

3 years ago

Read 2 more answers

Keisha solved the following equation: 4x − 2x + 8 = 6(x + 4) Step Work Justification 1 2x + 8 = 6(x + 4) Combine like terms 2 2x

kolbaska11 [484]

4x - 2x + 8 = 6(x + 4) Given

(4x - 2x) + 8 = 6(x + 4)

2x + 8 = 6(x + 4) Combine like terms

2x + 8 = (6)(x) + (6)(4)

2x + 8 = 6x + 24 Distributive Property

2x - 6x + 8 = 6x - 6x + 24

-4x + 8 = 24 Subtraction Property of Equality

-4x + 8 - 8 = 24 - 8

-4x = 16 Subtraction Property of Equality

-4x : (-4) = 16 : (-4)

x = -4 Division Property of Equality

4 0

3 years ago

Evaluate:cos 45°/sec 30°+cosec30°​

Evaluate:cos 45°/sec 30°+cosec30°