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4 years ago

In the triangle ABC, if side a is 3, side b is 4 and side c is 5, what is the cosine of the smallest angle?

Mathematics

1 answer:

sashaice [31]4 years ago

5 0

Answer:

Cosine of the smallest angle is 4/5.

Step-by-step explanation:

It is given that in the triangle ABC, side a is 3, side b is 4 and side c is 5.

Sum of squares of two smaller sides.

$3^2+4^2=9+16=25$

Sum of squares of largest sides.

$5^2=25$

Since sum of squares of two smaller sides is equal to sum of squares of largest sides, therefore triangle ABC is a right angle triangle.

Hypotenuse = 5 units.

In a right angle triangle, the smallest angle has shortest opposite side.

Shortest side is a=3 It means angle A is smallest.

$\cos \theta = \dfrac{adjacent}{hypotenuse}$

$\cos (A) = \dfrac{AC}{AB}$

$\cos (A) = \dfrac{4}{5}$

Therefore, the cosine of the smallest angle is 4/5.

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If a = b and b = c, which statement must be true?

murzikaleks [220]

Answer:

D.- ac

Step-by-step explanation:

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3 years ago

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What are the domain and range of the inequality y < sqrt x+3+1

love history [14]

Given:

The inequality is:

$y$

To find:

The domain and range of the given inequality.

Solution:

We have,

$y$

The related equation is:

$y=\sqrt{x+3}+1$

This equation is defined if:

$x+3\geq 0$

$x\geq -3$

In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.

So, the domain of the given inequality is x>-3.

We know that,

$\sqrt{x+3}\geq 0$

$\sqrt{x+3}+1\geq 0+1$

$y\geq 1$

The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.

So, the domain of the given inequality is y>1.

Therefore, the correct option is A.

3 0

3 years ago

How do you find square roots? Example: Square root of 441.

Alecsey [184]

There isn't really a formula for higher numbers. you can use a calculator with the square root function

6 0

3 years ago

Prove the divisibility:<br><br>45^45·15^15 by 75^30

garri49 [273]

Answer:

$3^{75}$ .

Step-by-step explanation:

We have been an division problem: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(9*5)^{45}=9^{45}*5^{45}$

$15^{15}=(3*5)^{15}=3^{15}*5^{15}$

$75^{30}=(15*5)^{30}=15^{30}*5^{30}$

Substituting these values in our division problem we will get,

$\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}$

$\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}$

$\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}$

Using power rule of exponents $a^n*a^m=a^{n+m}$ we will get,

$\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}$

$\frac{3^{105}*5^{60}}{3^{30}*5^{60}}$

$\frac{3^{105}}{3^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{105}}{3^{30}}=3^{105-30}$

$3^{105-30}=3^{75}$

Therefore, our resulting quotient will be $3^{75}$ .

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3 years ago

A cylinder contain 150.8 cubic units of water. What is the minimum radius of a sphere that will hold the water? Round to nearest

Oksi-84 [34.3K]

70 because you would divide 150.8 by 2 and it gives you 75.4 but you have to round it and do v=4/3×3.14×70^3

6 0

3 years ago