In ABC, A=29°, B=36° , b=15•8cm, find a
a/sin 29 =15.8/sin 36
a/0.485=15.8/0.5877
a=15.8*0.485/0.5877
a=7.663/0.5877
a=13.038cm
Assuming you are following standard convention of naming angles and sides,
and assuming 15•8 means15.8
then we have a simple sine law situation:
a/sin29° = 15.8/sin36°
a = 15.8sin29·/sin36°
= ...
Answer the question
Well, well, well... looks like it's time for a little bit of trigonometry circus fun!
Now, to find side "a" in triangle ABC, we can use the Law of Sines, because we love our mathematical laws around here.
The Law of Sines states that the ratio of a side length to the sine of its opposite angle is the same for all sides in a triangle. So, let's get to calculating, shall we?
We have angle A as 29°, angle B as 36°, and side b as 15.8 cm. The opposite sides of these angles are a and c, respectively.
Let's start by finding side a:
First, let's find the sine of angle A:
sin(A) = (opposite side a) / (hypotenuse c)
But we don't know the hypotenuse just yet, so let's find it using the Law of Sines:
sin(B) / b = sin(A) / a
Plug in the values we know:
sin(36°) / 15.8 = sin(29°) / a
Now, let's solve for a:
a = (sin(29°) * 15.8) / sin(36°)
And after doing some fancy number crunching, we find that side a is approximately... tada! - 12.6 cm.
So, there you have it! Side a in triangle ABC is around 12.6 cm, ready to join the geometry circus. Enjoy the show!
To find side "a," we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
First, let's identify the given information:
- Angle A is 29°.
- Angle B is 36°.
- Side b is 15.8 cm.
Using the Law of Sines, we can set up the following equation:
a / sin(A) = b / sin(B)
Plugging in the values we have:
a / sin(29°) = 15.8 cm / sin(36°)
Now, let's solve for "a." First, we'll find the sine of 29° and 36°:
sin(29°) = 0.4848
sin(36°) = 0.5878
Then, substituting these values into the equation:
a / 0.4848 = 15.8 cm / 0.5878
Next, we'll isolate "a" by multiplying both sides of the equation by 0.4848:
a = (15.8 cm / 0.5878) * 0.4848
Calculating this expression:
a ≈ 12.289 cm
Therefore, side "a" is approximately 12.289 cm.