Your triangle has acute angles X and Y, and right angle Z.
For an acute angle A in a right triangle:
The sine is the ratio of the opposite leg to the hypotenuse.
sin A = opp/hyp
The cosine is the ratio of the adjacent leg to the hypotenuse.
cos A = adj/opp
The hypotenuse of a right triangle is the side opposite the right angle. It is the longest side of a right triangle. There is only one hypotenuse in a triangle, so there is no confusion with the hypotenuse.
The two sides that form the right angle are called the legs. Each leg is opposite an acute angle. The legs may or may not be congruent to each other, but each leg is always shorter than the hypotenuse. Since there are two legs, we need to be able to distinguish them. If you take an acute angle as your angle of interest, the leg that is part of the angle is called the adjacent leg. The other leg is the opposite leg. Adjacent leg and opposite leg are relative terms. They depend on the acute angle you are considering.
For your triangle, if you look at angle X, then the adjacent leg is side XZ. The opposite leg for angle X is side YZ.
Using the ratios mentioned above for sine and cosine, you get:
sin X = opp/hyp = sqrt(119)/12
cos X = adj/hyp = 5/12
Answer:
41.8°
Step-by-step explanation:
Resolvemos esta pregunta usando la regla del seno
a / sin A = b / sin B
Estamos despejando el ángulo B
Por lo tanto:
3 / sin 30 = 4 / sin B
Cruz multiplicar
3 × sin B = sin 30 × 4
sin B = sin 30 × 4/3
B = arco sin [sin 30 × 4/3]
B = 41.81031 °
Aproximadamente = 41.8 °
Answer:
4 Hours.
Step-by-step explanation:
You would set this up as an equality where x represent hours
19.00 + 1.50x = 14+2.75x
You then get the x on one side by subtracting 14 from both sides and 1.50x from both sides.
5 = 1.25x
Divide both sides by 1.25 to x by itself.
4 = x
9514 1404 393
Answer:
x = 10
Step-by-step explanation:
The marked sides are proportional, so we have ...
x/8 = (x +5)/12
3x = 2(x +5) . . . . . multiply by 24 to clear fractions
3x = 2x + 10 . . . . . eliminate parentheses
x = 10 . . . . . . . . . . subtract 2x
_____
<em>Alternate solution</em>
We observe that the difference between the upper segment lengths is ...
(x +5) -(x) = 5
and the difference between the lower segment lengths is ...
12 -8 = 4
This means the upper segment lengths are 5/4 times as long as the lower segments. Then ...
x = (5/4)(8) = 10
