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4 years ago

Simplify cos5cos40-sin5cos40

Mathematics

2 answers:

worty [1.4K]4 years ago

8 0

galben [10]4 years ago

3 0

Answer:

cos(5)cos(40) - sin(5)cos(40) = cos(45) = √(2)/2

Step-by-step explanation:

One of the trig identity (Angle Sum/Difference Identity) is:

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)

We're given: cos(5)cos(40) - sin(5)cos(40)

In this case, α=5 and β=40

Plug it into you're equation

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)

cos(5 + 40) = cos(5)cos(40) - sin(5)cos(40)

cos(5 + 40) = cos(45) = √(2)/2

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Find the base of the triangle whose area is 2.4 cm² and who is height is 1.6 cm

Karo-lina-s [1.5K]

Formula of the area of triangle: (BxH)/2

So:

1.6B/2 = 2.4

Multiply both sides by 2:

1.6B = 4.8

Divide both sides by 1.6:

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6 0

4 years ago

PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!

Elenna [48]

Answer:

$cos(V)=\frac{39}{89}=.44$

∠ $V=64.01$ °

Step-by-step explanation:

$sin(angle)=\frac{opposite}{hypotenuse}$

$cos(angle)=\frac{adjacent}{hypotenuse}$

$tan(angle)=\frac{opposite}{adjacent}$

The cosine of an angle is equal to the side adjacent to the angle over the hypotenuse, the longest side.

With this in mind:

$cos(V)=\frac{39}{hypotenuse}$

We need to find the hypotenuse of this triangle. This is relativly easy to do with a right triangle; we can just use the Pythagorean Theorem.
Pythagorean Theorem: $a^2+b^2=c^2$ where $a$ , $b$ , and $c$ are the 3 different sides of a right triangle.

$a^2+b^2=c^2\\(39)^2+(80)^2=c^2\\1521+6400=c^2\\c=\sqrt{7921} \\c=89$

Our hypotenuse is $89$ . Now we can finish solving for ∠ $V$ .

$cos(V)=\frac{39}{89}\\V=cos^-^1(\frac{39}{89})\\$

∠ $V=64.01$ °

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4 years ago

The hypotenuse of a right triangle is 26m and the sum of its legs is 34m. Find the legs.

marysya [2.9K]

Answer: If you need to find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem if you know the length of the other two sides. Square the length of the 2 sides, called a and b, then add them together. Take the square root of the result to get the hypotenuse

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3 years ago

An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20\text{ cm}d=20 cmd, equals, 20, s

aivan3 [116]

Answer: The answer is 314.28 cm² (approx.).

Step-by-step explanation: Given that an engineer is going to install a new water pipe. The diameter of this circular pipe is, d = 20 cm.

We need to find the area 'A' of the circular cross-section of the pipe.

Given, diameter of the circular section is

$\textup{d}=20~\textup{cm}.$