Answer this question

Calcula en cada caso las restantes razones trigonométricas de un angulo agudo si se conoce que:

olchik [2.2K]

A) cos a = (√22)/5; tan a = (√66)/22
B) sin a = (2√2)/3; tan a = 2√2
C) sin a = (√30)/6; cos a = (√6)/6
D) sin a = 3/5; tan a = 3/4
E) sin a = (5√26)/26; cos a = (√26)/26
F) sin a = 3/5; tan a = 3/4

Explanation
The ratio for sine is opposite/hypotenuse. This means the side opposite the angle is √3 and the hypotenuse is 5. Using the Pythagorean theorem to find the adjacent side,
(√3)² + A² = 5²
3+A² = 25
A² = 22
A=√22
This means that cos a = adjacent/hypotenuse = (√22)/5 and tan a = opposite/adjacent = (√3)/(√22) = (√66)/22.
B) The ratio for cosine is adjacent/hypotenuse; this means the side adjacent to the angle is 1 and the hypotenuse is 3. Using the Pythagorean theorem to find the side opposite the angle (p),
1² + p² = 3²
1+p² = 9
p² = 8
p=√8 = 2√2
This means that sin a = opposite/hypotenuse = (2√2)/3 and tan a = opposite/adjacent = (2√2)/1 = 2√2.
C) The ratio for tangent is opposite/adjacent; this means that the side opposite the angle is √5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
(√5)²+1² = H²
5+1=H²
6=H²
√6 = H
This means that sin a = opposite/hypotenuse = (√5)/(√6) = (√30)/6 and cos a = adjacent/hypotenuse = 1/(√6) = (√6)/6.
D) The ratio for cosine is adjacent/hypotenuse; this means that the side adjacent the angle is 4 and the hypotenuse is 5. Using the Pythagorean theorem to find the side opposite the angle, p:
4²+p²=5²
16+p²=25
p²=9
p=3
This means that sin a = opposite/hypotenuse = 3/5 and tan a = opposite/adjacent = 3/4.
E) The ratio for tangent is opposite/adjacent;; this means that the side opposite the angle is 5 and the side adjacent the angle is 1. Using the Pythagorean theorem to find the hypotenuse,
5²+1²=H²
25+1=H²
26=H²
√26 = H
This means that sin a = opposite/hypotenuse = 5/(√26) = (5√26)/26 and cos a = adjacent/hypotenuse = 1/(√26) = √26/26.
F) 0.8 = 8/10; The ratio for cosine is adjacent/hypotenuse. This means that the side adjacent the angle is 8 and the hypotenuse is 10. Using the Pythagorean theorem to find the side opposite the angle, p:
8²+p² = 10²
64+p² = 100
p² = 36
p=6
This means that sin a = opposite/hypotenuse = 6/10 = 3/5 and tan a = opposite/adjacent = 6/8 = 3/4.

6 0

3 years ago

Read 2 more answers

How do you find the scale factor of two triangles, 0.3 and 2.4?

bagirrra123 [75]

Divide the larger one by the smaller one. 2.4 divided by 0.3 gives you 8. That means the scale factor is 8, or the larger triangle is 8 times larger than the smaller. We can prove this by multiplying 0.3 by 8 and getting 2.4

8 0

3 years ago

Sutopa has 3/4 of the money Maneet has. Maneet has $18 less than Kim. Together, they have $286.40. How much money does each of t

anastassius [24]

Solving a system of equations we can see:

Sutopa has $73.20
Maneet has $97.60
Kim has $115.60

<h3>How much money each of them has?</h3>

First, let's define the variables:

S = money that Sutopa has.
M = money that Maneet has.
K = money that Kim has.

We can write the system of equations:

S = (3/4)*M

M = K - $18

S + M + K = $286.40

First, we can rewrite the second equation to get:

K = M + $18

Now we can replace the first and second equations into the third one:

(3/4)*M + M + (M + $18) = $286.40

Now we can solve this for M:

M*(1 + 1 + 3/4) = $286.40 - $18

M = $268.40*(4/11) = $97.60

Now we can find the other two values:

K = M + $18 = $97.60 + $18 = $115.60

S = (3/4)*M = (3/4)*$97.60 = $73.20

If you want to learn more about systems of equations:

brainly.com/question/13729904

#SPJ1

6 0

2 years ago

Kate swam 18 laps at practice This is three fourths The number Of laps that paco swam at practice write an equation that can be

Lunna [17]

18÷4=5×3=15 laps that paco swam

5 0

3 years ago

FInd the solution for 4(x - 5)=2(x - 10) +2x

crimeas [40]

Hello!

You solve this like an algebraic equation

You first distribute the 4 and 2

4x - 20 = 2x - 20 + 2x

Combine like terms

4x - 20 = 4x - 20

subtract 4x from both sides

-20 = 0x - 20

Add 20 to both sides

0 = 0

This means that there are infinite solutions to the equation.

Hope this helps!

3 0

3 years ago

Read 2 more answers